Practice Test

Q1) Torques of equal magnitude are applied to a solid sphere and a solid cylinder both having same mass and radius . The cylinder is free to rotate about its axis while sphere is free to rotate about its diameter. What is the ratio of the angular acceleration acquired after a given time? Show Answer

Q2) In the above question the minimum coefficient of friction is : Show Answer

Q3) A body rolls down an inclined plane. If its K.E. of rotational is 40% of the translational K.E. ., then the body is: Show Answer

Q4) A particle of mass m slides down an inclined plane and reaches the bottom with liner velocity v. If the same mass is in the form of ring and rolls without slipping down the same inclined plane, its velocity will be: Show Answer

Q5) A solid disc first rolls without slipping and then slides without rolling down the same inclined plane. The velocities in two cases at the bottom are in the ratio of: Show Answer

Q6) The moment of inertia of two spheres of equal masses about their diameter are equal. If one of them is solid and other is hollow , the ratio of their radii is: Show Answer

Q7) Moment of inertia of a hoop about an axis passing through the rim and perpendicular to its plane and moment of inertia about its diameter bears a following ratio with each other: Show Answer

Q8) If earth suddenly contract to half of its radius without change in its mass, the length of the day will become: Show Answer

Q9) What should be the ratio between the length and radius of the uniform solid cylinder so that its moment of inertia about central axis is the same as that about equatorial axis? Show Answer

Q10) A solid cylinder of mass m and radius R rolls down an inclined plane without slipping. The speed of its center of mass at the bottom is: Show Answer

Q11) Four identical sphere each of radius 20 cm and mass 1 kg are placed on a horizontal touching each other so that their centres are located at the corners of square of side 40 cm, What is the distance of their center of mass from the center of either sphere ? Show Answer

Q12) A mass sliding down an inclined plane and reaches the bottom with velocity v . If the same mass is in the form of a disc and rolls down the same inclined plane, What is its velocity at the bottom? Show Answer

Q13) Moment of inertia of two sphere, one solid and other hollow ,having equal radii, is equal . If mass of solid is 5 kg, What is the mass of hollow? Show Answer

Q14) The M.I of a circular loop radius R and mass M about any line tangential to the ring is: Show Answer

Q15) A mass is whirled in a circular path with constant angular velocity and its angular momentum is L. If the string is now halved keeping the angular velocity same, the angular momentum is: Show Answer

Q16) Four sphere of radius 'r' each and mass m are placed with their centers on the four corners of the square of side 'a' The M.I. of the system about an axis along one of the sides of square is: Show Answer

Q17) M. I of uniform disc about one of diameter is I.Its M.I. about an axis perpendicular to its plane and passing through a point on its rim will be: Show Answer

Q18) Two bodies of masses m and 3 m are connected by a light string passing over a smooth pulley. During the ensuing motion the acceleration of the center of mass is: Show Answer

Q19) A solid cylinder first rolls without slipping and then slides without rolling down the same inclined plane. The ratio of velocities in the two cases at the bottom of the plane is: Show Answer

Q20) A meter stick is held vertically with one end on the floor and is allowed to fall. What is the velocity with which the other end hits the floor, assuming that lower end does not slip? Show Answer

Q21) A rope dancer standing on a platform rotating about vertical axis passing through its center. She pulls her arm towards the body reducing her M.I. by a factor n. The angular speed is proportional to: Show Answer

Q22) A uniform disc of mass m and radius R rotates about frictionless axle passing through its center and perpendicular to its plane. A chord is wound over the rim of the disc. A uniform force F is applied to the other end of chord. The tangential acceleration is proportional to: Show Answer

Q23) The angular velocity of a body change from one revolution per 25 second to one revaluation per second without applying any torque. The ratio of its radius of gyration in two cases is: Show Answer

Q24) From a given sample of uniform wire , two circular loops P and Q are made, P of radius 'r' and Q of radius nr. If the M.I. of Q about its axis is 4 times the value of n is: Show Answer

Q25) A rod of length L whose lower end is sliding along the horizontal plane, starts to topple form vertical position. The velocity of the upper end when it hits the ground is: Show Answer

Q26) A particle performs uniform circular motion with angular momentum L. If the frequency of motion is doubled and its K.E. is halved , the angular momentum becomes: Show Answer

Q27) A solid cylinder rolls down an inclined plane. It has sufficient friction to prevent sliding. The ratio of rotational energy to the total K. E. is: Show Answer

Q28) The angular velocity of body changes from 1 revolution per 16 seconds to 1 rev. per sec. without applying an external torque. The ratio of radii of gyration in two cases is: Show Answer

Q29) A particle is making uniform circular motion with angular momentum J. If its K.E. is made half and angular frequency is doubled, its new angular momentum is: Show Answer

Q30) A solid and a hollow cylinder of same mass, radius, length are released from the same height at the same time on an inclined plane. They roll down without slipping. Which one reaches the bottom first? Show Answer

Q31) A solid cylinder and a hollow cylinder both of the same mass and same external diameter are released from the same hight at the same time on an include plane. Both roll down without slipping. Which one wil reach the bottom first?
Show Answer

Q32) Which of the following statements about angular momentum is correct? Show Answer

Q33) The M.I. of a disc of mass 0.4 kg and radium 1 m about an axis perpendicular to the plane of the disc and passing though its centre is : Show Answer

Q34) If I is the moment of inertia and E is the kinetic energy of rotation of a body, then its angular momentum will be:
Show Answer

Q35) A solid sphere of mass M and radius R spine about an axis passing through its centre making 600b r.p.m. Its kinetic energy of rotation is : Show Answer

Q36) From a given sample of a uniform wire two loops are made P of radium r and Q of radius nr. If the M.I. of Q is 4 times that of about their natural axes value of 'n' is :
Show Answer

Q37) A solid sphere of radius R is placed on smooth horizontal surface. A horizontal force 'F' is applied at height h from the lowest point. For the maximum acceleration of centre of mass, which is correct ?
Show Answer

Q38) A rod of length is 3m and its mass acting per unit length is directly proportional to distance x from one of its end then its centre of gravity from that end will be at: Show Answer

Q39) The angular momentum of a moving body remains constant if: Show Answer

Q40) Two blocks of masses 10 kg and 4 kg are connected by a negligible mass and placed on a friction less horizontal surface. An impulse gives a velocity of 14m/s to the heavier block in the direction of the lighter block. The velocity of the centre of mass is: Show Answer

Q41) A wire of length l is bent ion the form of a circular ring, the moment of inertia about its axis is: Show Answer

Q42) A ballet dancer is spinning about a vertical axis with an angular velocity of 20 rad/s.If she suddenly changes her angular velocity to 10 rad/s, the new moment of inertia would be (I is initial moment of inertia) Show Answer

Q43) A solid sphere (mass 2M) and a thin spherical shell (mass M) both of the same size, roll down a inclined plane , then: Show Answer

Q44) A ball rolls without slipping. The radius of gyration of the ball about an axis passing through its centre of mass is K. If radius of the ball be R, then the fraction of total energy associated with its rotational energy will be: Show Answer

Q45) A solid cylinder of mass M and radius R without slipping down an inclined plane of length L and height h. What is the speed of centre of mass when the cylinder reaches bottom? Show Answer

Q46) To move a body in a circle, which of the following forces is needed? Show Answer

Q47) Five particles of mas 2kg are attached to the rim of circular disc of radius 0.1 m and negligible mass. Moment of inertia of the system about the axis passing through the center of the disc and perpendicular to its plane is: Show Answer

Q48) A sphere of diameter 0.2 m and mass 2 kg is rolling on a inclined plane with velocity v = 0.5 m/s. The kinetic energy of the sphere is: Show Answer

Q49) The motion of planes in the solar system is an example of the conservation of: Show Answer

Q50) A solid cylinder of radius r rolls down on an inclined plane without slipping. The speed of the centre of mass when its reaches the bottom ,is: Show Answer

Q51) The ratio of radii of two spheres of the same mass, having the same moment of inertia about their diameters one hollow and other solid is: Show Answer

Q52) A child is standing with folded hands at the centre of a platform rotating about its central axis. The kinetic energy of the system is k. The child axis. The child now stretches his arms so that the moment of inertia of the system doubles. The kinetic energy of the system now is: Show Answer

Q53) The ratio of the radii of gyration of a circular disc about a tangential axis in the plane of the disc and of a circular ring of the same radius about a tangential axis in the plane of the ring is: Show Answer

Q54) Angular momentum of a body is defined as the product of: Show Answer

Q55) Moment of a couple is called: Show Answer

Q56) The ratio of the radii of gyration of a circular disc to that of a circular ring, each of same mass and radius. around their respective axes is: Show Answer

Q57) Two bodies have their moments of inertia I and 2 I respectively about their axis of rotation. If their Kinetic energies of rotation are equal, their angular momenta will be in the ratio: Show Answer

Q58) From a circular disc of radius R and mass 9 M, a small of radius R/3 is removed. The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through O is: Show Answer

Q59) The moment of inertia of a uniform circular disc of radius 'R' and mass 'M' about an axis passing from the edge of the disc and normal to the disc is: Show Answer

Q60) The M.L of a uniform circular disc of radius 'R' and mass 'M'' about an axis touching the disc at its diameter and normal to the disc is: Show Answer

Q61) A solid sphere of mass M and radius R having M.I I about its diameter is recaste into a solid disc of radius r and thickness 't'.The M.I of this disc about an axis passing through the edge and perpendicular to its pane remains I. Then 'R' and 'r' relate as: Show Answer

Q62) Two particles which are initially at rest move towards each other under the action of their internal attraction. If their speeds are v and 2 v at any instant then the speed of center of mass of the system will be: Show Answer

Q63) A particle is moving in a horizontal circle of radius r, with a uniform speed v. In moving from a point on the circle to a diametrically opposite point, its Show Answer

Q64) In which accelerated motion, the kinetic energy of a particle remain constant? Show Answer

Q65) A particle is acted upon by a force of constant magnitude, which is always perpendicular to the velocity of the particle. The motion of the particle takes place in a horizontal plane. Then it follows that Show Answer

Q66) The angular speed of the minute hand of a clock in degrees per second is Show Answer

Q67) A particle is performing a U.C.M. along a circle of radius R. In half the period of revolution, its displacement and distance covered are Show Answer

Q68) The angular speed of a flywheel rotating at 90 r.p.m. is Show Answer

Q69) What is the angular acceleration of a particle in circular motion, which slows down from 600 r.p.m. to rest in 10s? Show Answer

Q70) The angular velocity of the earth due to its spin motion is: Show Answer

Q71) If the frequency of a particle performing circular motion increases from 60 rpm to 180 rpm in 20 seconds, its angular acceleration is: Show Answer

Q72) A flywheel rotates at a constant speed of 2400 rpm. The angle described by the shaft in radian in one second is: Show Answer

Q73) Particle A of mass M is revolving along a circle of radius R. Particle B of mass m is revolving in another circle of radius r. If they take the same time to complete one revolution, then the ratio of their angular velocities is Show Answer

Q74) Two particles of masses M and m revolve in circular orbits of radii R and r. If the time periods of both the particles are equal, then the ratio of their linear speed is Show Answer

Q75) The length of the second hand of a watch is 1 cm. What is the velocity of the tip of the second hand in cm/s? Show Answer

Q76) The angular velocity of a geostationary satellite is Show Answer

Q77) A particle moves along a circle of radius 10 cm. If its linear speed changes from 4 m/s to 5 m/s in 1 s, then its angular acceleration will be Show Answer

Q78) The angular velocity of a fly wheel increases from 0 to 40 rad/s, in 8 second. What is its total angular displacement in this time? Show Answer

Q79) A wheel rotates with a constant angular velocity of 600 r.p.m. What is the angle through which the wheel rotates in one second? Show Answer

Q80) What is the angular displacement of the minute hand of a clock in 600 seconds? Show Answer

Q81) A particle moves along a circular path of radius r with uniform speed v. The angle described by the particle in one second is Show Answer

Q82) The relative angular speed of the minute hand and second hand of a clock is Show Answer

Q83) The average acceleration vector for a particle having a uniform circular motion is Show Answer

Q84) An object is moving in a circle of radius 100 m with a constant speed of 3.14 m/s. What is the average speed for one complete revolution? Show Answer

Q85) A particle performing a U.C.M. of radius pi m makes 'p' revolutions in 't' seconds. What is its tangential velocity? Show Answer

Q86) Angular speed of the hour hand of a clock in degree per second is Show Answer

Q87) A particle rotates in U.C.M. with tangential velocity 'v' along a horizontal circle of diameter 'D'. Total angular displacement of the particle in time 't' is Show Answer

Q88) A particle is moving with a constant speed v in a circle of radius R. What is the magnitude of average acceleration after half revolution? Show Answer

Q89) If the momentum of a body is increased by 20%, then its kinetic energy increases by Show Answer

Q90) A 4 kg mass and a 1 kg mass are moving with equal energies. The ratio of the magnitudes of their linear momenta is Show Answer

Q91) A body moving in a circular path with a constant speed has a Show Answer

Q92) A car is travelling on a circular track of radius 100 m, at a constant speed. What is its average velocity and average speed when it completes one revolution in 62.8 s? Show Answer

Q93) What is the angular velocity of the hour hand of a clock? Show Answer

Q94) Which one of the following has the maximum angular velocity? Show Answer

Q95) A body is moving along a horizontal circular path with constant speed v. What is the change in its velocity when it describes an angle theta? Show Answer

Q96) The angular velocity of a wheel increases from 600 rev/min to 2400 rev/min in 10 sec. The number of revolutions made during this time interval is Show Answer

Q97) The linear velocity of a body, moving on the circumference of a circle of radius r, is equal to the velocity acquired by a freely falling body in covering a distance equal to half the radius of the circle. Then the centripetal acceleration of the body is Show Answer

Q98) A particle P is moving in a circle of radius r with uniform speed v. C is the centre of the circle and AB is the diameter. What is the ratio of the angular velocities of P about A and C? Show Answer

Q99) A particle is moving in a circle of radius 1.5 m. Its speed is increasing by 180 rev/minute in one minute. What is its linear acceleration? Show Answer

Q100) Identify the wrong statement from the following: Show Answer

Q101) The length of the second's hand in a watch is 1 cm. What is the change in velocity of its tip in 15 second? Show Answer

Q102) A body of mass m performs uniform circular motion along a circular path of radius r with a velocity v. If its angular momentum is L, then the centripetal force acting on it is Show Answer

Q103) The motor of an engine is rotating about its axis, with an angular velocity of 120 rpm. After being switched off, it comes to rest in 16 s. How many revolutions will it perform before coming to rest, if it has a constant angular deceleration? Show Answer

Q104) A body of mass m is performing a U.C.M., in a circle of radius r. The work done by the centripetal force, in moving it through 1/3 of the circular path is Show Answer

Q105) A body is moving along a circular path with a constant speed. It has a centripetal acceleration (a). If its speed is doubled, the ratio of its acceleration after and before the change is given by Show Answer

Q106) A body is revolving with a constant speed along a circle, in the clockwise direction. If it starts moving in the anti- clockwise direction, then Show Answer

Q107) The angle between the radius vector and the centripetal force is Show Answer

Q108) The overbridge on a canal is in the form of concave circular arc of radius r. The thrust on the road at the lowest point will be Show Answer

Q109) A car of mass m has to cross an overbridge, which is convex upwards. If the radius of the bridge is r and the speed of the car is v, then the thrust on the bridge at the highest point will be Show Answer

Q110) Two satellites A and B are revolving around the earth with the same angular speed. If they are at heights of 300 km and 500 km respectively, then the centripetal acceleration will be Show Answer

Q111) A 0.5 kg mass is rotated in a horizontal circle of radius 20 cm. If its angular speed is 0.8 rad/s, the centripetal force acting on it is: Show Answer

Q112) A car is accelerating at a rate 'a' in a horizontal direction. A simple pendulum is hung from the ceiling of the car. The time period of oscillation of the pendulum is given by Show Answer

Q113) A particle moves along a circle of radius 'r' with constant tangential acceleration. If the velocity of the particle is 'v' at the end of second revolution, after the revolution has started then the tangential acceleration is Show Answer

Q114) If P is the magnitude of linear momentum of a particle executing a uniform circular motion, the centripetal force acting on the particle is given by Show Answer

Q115) A mass of 2 kg is whirled in a horizontal circle by means of a string at an initial speed of 5 revolutions per minute. Keeping the radius constant, the tension in the string is doubled. The new speed is nearly equal to Show Answer

Q116) Which one of the following forces is a pseudo force? Show Answer

Q117) A coin placed on a rotating gramophone disc, remains at rest when it is at a distance of 9 cm from its centre. The angular velocity of the disc is then tripled. At what distance from the centre, the coin should be placed, so that it will remain at rest? Show Answer

Q118) A bottle of soda water is grasped by the neck and swung briskly in a circle. Near which portion of the bottle do the bubbles collect? Show Answer

Q119) A particle performs a uniform circular motion in a circle of radius 10 cm. What is its centripetal acceleration if it takes 10 seconds to complete 5 revolutions? Show Answer

Q120) If a cycle wheel of radius 0.4 m completes one revolution in one second, then the acceleration of a point on the rim is Show Answer

Q121) A stone of mass 250 gram, attached at the end of a string of length 1.25 m is whirled in a horizontal circle at a speed of 5 m/s. What is the tension in the string? Show Answer

Q122) A particle is performing a U.C.M. along a circular path of radius r, with a uniform speed v. Its tangential and radial acceleration are Show Answer

Q123) A particle of mass 'm' moves with a constant speed along a circular path of radius r under the action of a force F. Its speed is given by Show Answer

Q124) A particle is performing a U.C.M. along a circle of radius r. The relation between its centripetal acceleration (a) and kinetic energy (E) is given by Show Answer

Q125) A cosmonaut is orbiting the earth in a spacecraft at an altitude h = 630 km with a speed of 8 km/s. The radius of the earth is 6400 km. What is the approximate value of the acceleration of the cosmonaut? Show Answer

Q126) A particle moves with constant speed v along a circular path of radius r and completes the circle in time T. What is the acceleration of the particle? Show Answer

Q127) A stone of mass 16 kg is attached to a string 144 m long and is whirled in a horizontal circle. The maximum tension the string can stand is 16 newton. The maximum velocity of revolution that can be given to the stone without breaking it will be Show Answer

Q128) A sphere of mass m is tied to one end of a string of length I and rotated through the other end along a horizontal circular path with speed V. The work done in full horizontal circle is Show Answer

Q129) A body describes a circular path of radius 10 m, with a uniform speed. If it is acted upon by a centripetal force of 0.4 newton, then the kinetic energy of the body will be Show Answer

Q130) A flywheel of diameter 1 m is rotating at 600 r.p.m. The acceleration of a point on the rim of the fly wheel is Show Answer

Q131) When a body performs a U.C.M. its tangential acceleration is Show Answer

Q132) A particle of mass m is moving along a circular path of radius r, with uniform speed v. The relation between its kinetic energy (E) and momentum (P) is given by Show Answer

Q133) A wheel is rotating about an axis passing through its centre and perpendicular to its plane. If its angular speed is slowly increased then a point on its rim has Show Answer

Q134) A particle moves in a circular orbit under the action of a central attractive force which is inversely proportional to the distance 'r'. The speed of the particle is Show Answer

Q135) A coin kept on a rotating gramophone disc just begins to slip if its centre is at a distance of 8 cm from the centre of the disc. The angular velocity of the gramophone disc is then doubled. Through what distance, the coin should be shifted towards the centre, so that the coin will just slip? Show Answer

Q136) A long beam is spun at a constant speed of 1.75 rad/s. During the period of training, an astronaut is made to walk slowly along this beam, away from the axis of rotation. At what distance, from the axis of rotation, he will experience a centrifugal acceleration equal to the acceleration due to gravity? Show Answer

Q137) A motor cycle is going on a overbridge of radius R. The driver maintains a constant speed. When the motor cycle ascends on the overbridge, the normal force (reaction) acting on it Show Answer

Q138) A particle describes a horizontal circle of radius r in a conical funnel, with smooth inner surface with a speed of 0.5 m/s. What is the height of the plane of the circle from the vertex of the funnel? Show Answer

Q139) A body of mass m is tied to one end of a spring and whirled round in a horizontal circle with a constant angular velocity. The elongation in the spring is 1 cm. If the angular velocity is doubled, the elongation in the spring is 5 cm. What is the original length of the spring? Show Answer

Q140) Which one of the following statements is wrong for a particle moving in a circle with a constant angular speed? Show Answer

Q141) A particle moves in a circle of radius 2 m at a speed given by v = 4t where v is in m/s and t is in second.
What is its resultant (total) acceleration at time t = 1s? Show Answer

Q142) A particle of mass m is performing a U.C.M. along a circular path of radius r. Its angular momentum about the axis of rotation (axis of the circle) is L. What is the kinetic energy of the particle? Show Answer

Q143) A cyclist has to bend inwards while taking a turn but a passenger sitting inside a car and taking the same turn is pushed outwards. This is because Show Answer

Q144) A car takes a turn on a slippery road at a safe speed of 9.8 m/s. If the coefficient of friction is 0.2, the minimum radius of the arc in which the car takes a turn is Show Answer

Q145) A man with his hands in his pockets is standing in a bus, which is taking a turn in a horizontal curve of radius 50m, with a speed of 7 m/s. How far from the vertical must he lean to keep his balance? Show Answer

Q146) What would be the maximum speed of a car on a road turn of radius 30 m, if the coefficient of friction between the tyres and the road is 0.4? Show Answer

Q147) The radius of curvature of a metre gauge railway line at a place, where the train is moving with a speed of 10 m/s is 50 m. If there is no side thrust on the rails, than the elevation of the outer rail above the inner rail is Show Answer

Q148) A cyclist moves in a circular track of radius 100 m. If the coefficient of friction is 0.2, then the maximum velocity with which the cyclist can take the turn with leaning inward is Show Answer

Q149) The radius of a curved path on a national highway is R. The width of the road is b. The outer edge of the road is raised by 'h' w.r.t. the inner edge, so that a car with a velocity V can safely pass over it. What is the value of h? Show Answer

Q150) The minimum velocity (in m/s) with which a car driver must traverse a flat curve of radius 150 m and coefficient of friction 0.6 to avoid skidding is Show Answer

Q151) Banking of roads is independent of Show Answer

Q152) The angle of banking is independent of Show Answer

Q153) Without changing the angle of banking, if we want to increase the maximum safe speed, with which a car can travel on the curved road by 10%, then we have to increase the radius of curvature of the road from 20 m to Show Answer

Q154) On a dry road, the maximum safe speed for a vehicle moving on a curved road is 30 km/hour. After heavy showers, the maximum safe speed for the same road was 18 km/hour. The ratio of the coefficient of friction for the dry road to that of wet road is Show Answer

Q155) A body of mass 1 kg is suspended from a string 1 m long. It is rotated in a vertical circle. What is the tension in the string, when it is horizontal and the speed of the body is 2 m/s? Show Answer

Q156) A body attached at one end of a string crosses the topmost point of a vertical circle with the critical speed. Its centripetal acceleration, when the string is horizontal will be Show Answer

Q157) A mass m is kept hanging by a rod of length L. What tangential velocity must be given to it so that it can just reach the top of the vertical circle? Show Answer

Q158) To describe a vertical circle of radius 20 cm, the minimum speed of a particle at the lowest point of the circle is 10 cm/s. If the radius of the circle is reduced to 1/4 of its original value, then the corresponding minimum speed will be Show Answer

Q159) If T and T' are the periods of a simple pendulum and a conical pendulum of the same length, then Show Answer

Q160) A motor cyclist loops a vertical circular loop of diameter 18 m, without droping down, even at the highest point of the loop. What should be his minimum speed at the lowest point of the loop? Show Answer

Q161) A small body attached at the end of an inextensible string completes a vertical circle, then its Show Answer

Q162) A body of mass 500 gram is rotating in a vertical circle of radius 1 m. What is the difference in its kinetic energies at the top and the bottom of the circle? Show Answer

Q163) A motor cyclist, in a circus, drives in a vertical loop inside a death well. What is the minimum speed required to complete the vertical circle, without falling down at the highest point, if the radius of the death well is 5 m? Show Answer

Q164) A body is allowed to slide down a frictionless inclined track under gravity from a height of 10 cm. The track ends in a circular loop of diameter D. The body is just able to complete the circular track, then the diameter of the track will be Show Answer

Q165) A bucket full of water is rapidly rotated in a vertical circle of radius r. It is found that the water does not fall down from the bucket, even when the bucket is inverted at the highest point, if it has a minimum critical speed at the highest point. If it continues with this speed, then the normal contact force exerted by the bucket on the water, at the lowest point in its path is Show Answer

Q166) A roller coaster is designed such that riders experience "weightlessness" as they go round the top of a hill whose radius of curvature is 20 m. The speed of the car at the top of the hill is between Show Answer

Q167) A particle of mass m is rotated in a vertical circle by means of a string. The difference in the tensions in the string at the bottom and the top of the circle would be Show Answer

Q168) A stone of mass m is tied to a string of length L and moved in a vertical circle at the rate of n revolutions/minute. The tension in the string when it is at its lowest point is Show Answer

Q169) What is the apparent weight of a body of mass m attached at the end of a string and which is just completing the loop in a vertical circle, at the lowest point in its path? Show Answer

Q170) A body is just being revolved in a vertical circle of radius R. The string breaks when the body is at the highest point. What is the horizontal distance covered by the body after the string breaks? Show Answer

Q171) The bulging of the earth at the equator and flattening at the poles is due to Show Answer

Q172) A car of mass 1500 kg rounds a curve of radius 250 m, at 90 km/hour. What is the centripetal force acting on it? Show Answer

Q173) In vertical circular motion, the ratio of the kinetic energy of a particle at the highest point to that at the lowest point is Show Answer

Q174) For a particle moving in vertical circle, the total energy at different positions along the path Show Answer

Q175) The physical quantity in transnational motion, which is analogous to moment of inertia in rotational motion is Show Answer

Q176) Two masses of 500 gram and 600 gram are attached to the 10 cm and 80 cm marks respectively of a light metre scale. The moment of inertia of this system about an axis passing through the centre of the scale will be Show Answer

Q177) A rod 0.5 m long has two masses each of 20 gram stuck at its ends. If the masses are treated as point masses and if the mass of the rod is neglected, then the moment of inertia of the system about a transverse axis passing through the centre is Show Answer

Q178) A wheel of mass 10 kg and radius of gyration 50 cm is rotating at 300 rpm. The rotational kinetic energy of the wheel is Show Answer

Q179) A disc of mass 1 kg and radius 10 cm is rotating about its axis with an angular velocity of 2 rad/s. The linear momentum of the disc, Show Answer

Q180) Three point masses each of mass m are situated at the corners of an equilateral triangle of side b. The moment of Inertia of the system about an axis coinciding with one of the sides is Show Answer

Q181) A circular disc is to be made by using equal masses of aluminium and iron. To get maximum moment of inertia, about its geometrical axis, it should be so prepared that Show Answer

Q182) A metre stick made of half wood and half steel is pivoted at the wooden end and a force is applied perpendicular to its length at the steel end. Then the stick is pivoted at the steel end and the same force is applied at the wooden end. The angular acceleration produced is Show Answer

Q183) When a rigid body is in motion, few particles of the body remain at rest at all times. What kind of motion is the rigid body having? Show Answer

Q184) If a horizontal cylindrical tube, partly filled with water is rapidly rotated about a vertical axis passing through its centre, the moment of inertia of the water about its axis will Show Answer

Q185) A flywheel rotating about a fixed axis has a kinetic energy of 225 J when its angular speed is 30 rad/s. What is the moment of inertia of the flywheel about its axis of rotation? Show Answer

Q186) A wheel of mass 4 kg and radius of gyration 0.4 m is making 300 r.p.m. Its moment of inertia is Show Answer

Q187) A flywheel rotating about a fixed axis has a kinetic energy of 360 Joule, when its angular speed is 30 rad/sec. The moment of inertia of the flywheel about the axis of rotation is Show Answer

Q188) A circular disc of mass 2 kg and radius 0.1 m is rotating at an angular speed of 2 rad/s, about an axis passing through its centre and perpendicular to its plane. What is its rotational kinetic energy? Show Answer

Q189) When the speed of a flywheel is increased from 240 r.p.m. to 360 r.p.m., the energy spent is 1936 J.
What is the moment of inertia of the flywheel? Show Answer

Q190) The moment of inertia about an axis of a body which is rotating with angular velocity 1 rad/s is numerically equal to Show Answer

Q191) A thin metal disc of mass 2 kg starts from rest and rolls down a smooth inclined plane. Its rotational K.E. is 4 J at the bottom of the inclined plane. What is its linear velocity at the same point? Show Answer

Q192) There are two eggs, one is a raw egg and the other is half boiled. They have identical sizes, shapes and weights. Then the ratio of the moment of inertia of half boiled egg to the raw egg about the central axis is Show Answer

Q193) When a disc rotates with uniform angular velocity, which of the following is not true? Show Answer

Q194) A heavy body and a light body have equal K.E. which one of them has greater momentum? Show Answer

Q195) If the angular velocity of a body increases by 20%, then its kinetic energy of rotation will increase by Show Answer

Q196) The angular velocity of a body is increased from 5 rad/s to 20 rads/s, without applying a torque but by changing its moment of Inertia. What is the relation between the new radius of gyration and the initial radius of gyration? Show Answer

Q197) A body rolls down a smooth inclined plane. If its rotational kinetic energy is 40% of its translational K.E., then the body must be a Show Answer

Q198) A car is moving with a constant speed. The wheels of the car make 120 rotations per minute. The brakes are applied and the car comes to rest in 8 second. How many rotations are completed by the wheels, before the car is brought to rest? (Assume that the brakes produce a constant retarding force) Show Answer

Q199) The ratio of the dimensions of Planck's constant (h) and the moment of inertia (I) is the dimension of Show Answer

Q200) The moment of inertia of a copper disc, rotating about an axis passing through its centre and perpendicular to its plane Show Answer

Q201) Four point masses, each of value m, are placed at the corners of a square ABCD, having each side of length L. What is the moment of inertia of this system about an axis passing through A and parallel to the diagonal BD? Show Answer

Q202) The diameter of a disc is increased by 2% without changing its mass. What is the percentage increase in its moment of inertia about its axis of symmetry? Show Answer

Q203) A molecule consists of two atoms each of mass m and separated by a distance d. If K is the average rotational K. E. of the molecule at particular temperature, then its angular frequency is Show Answer

Q204) When a ceiling fan is switched off, its angular velocity reduces to half its initial value after it completes 36 rotations. What is the number of rotations it will make further before coming to rest? (Assume that the angular retardation is uniform.) Show Answer

Q205) An automobile engine develops a power of 100 kilowatt, when rotating at a speed of 30 rev/sec. What torque does it deliver? Show Answer

Q206) Under a constant torque, the angular momentum of a body changes from 2x to 5x in 8 sec. The torque acting on the body is Show Answer

Q207) A torque of 100 N-m acting on a wheel at rest rotates it through 200 radian in 10 s. What is the moment of inertia of the wheel? Show Answer

Q208) A rope of negligible mass is wound around a hollow cylinder of mass 4 kg and radius 40 cm. What is the angular acceleration of the cylinder, if the rope is pulled with a force of 4 N? Assume that there is no slipping. Show Answer

Q209) Which one of the following relations is wrong? Show Answer

Q210) What is the power of an engine, if it applies a torque of 180 Nm, to rotate a rotor at a uniform angular speed of 100 rad/s? Show Answer

Q211) A rope is wound round a hollow cylinder of mass 5 kg and radius 0.5 m. What is the angular acceleration of the cylinder if the rope is pulled with a force of 20 N? Show Answer

Q212) A ring and a disc of different masses are rotating with the same kinetic energy. If a retarding torque (tau) is applied to the ring, the ring stops after completing n rotations. If the same retarding torque is applied to the disc, how many rotations would it complete before coming to rest? Show Answer

Q213) A rope is wound round a hollow cylinder of mass M and radius R. If the rope is pulled with a force F newton, then the angular acceleration of the cylinder will be Show Answer

Q214) A uniform disc of mass 500 kg and radius 2 metres is rotating at the rate of 600 rpm. What is the torque required to rotate the disc in the opposite direction with the same speed in a time of 100 seconds? Show Answer

Q215) A cord is wound around the circumference of wheel of radius 'r'. The axis of the wheel is horizontal and moment of inertia about it is 'I'. The weight 'mg' is attached to the end of the cord and falls from rest. After falling through a distance 'h', the angular velocity of the wheel will be Show Answer

Q216) A torque of 75 Nm acts on a body at rest for 4 s. What is the change in its angular momentum? Show Answer

Q217) A ring of mass 10 kg and radius 0.2 m is rotating about its geometrical axis at 20 rev/sec. Its moment of inertia is Show Answer

Q218) A rod of length 2 m, has a mass of 0.12 kg. Its moment of inertia about an axis passing through its one end and perpendicular to the length of the rod is Show Answer

Q219) A uniform disc of mass 5 kg has a radius of 0.5 m. Its moment of inertia about an axis passing through a point on its circumference and perpendicular to its plane is Show Answer

Q220) A rod of length 2 m has a mass of 0.24 kg. Its moment of inertia about an axis passing through its centre and perpendicular to the length of the rod is Show Answer

Q221) A disc of mass 2 kg is rolling on a horizontal surface without slipping with a velocity of 0.1 m/s. What is its rotational kinetic energy? Show Answer

Q222) A solid sphere of mass 1 kg and radius 10 cm rolls without slipping on a horizontal surface, with a velocity of 20 cm/s. The total kinetic energy of the sphere is Show Answer

Q223) Two rings have their M.I. in the ratio 2 : 1. If their diameters are in the ratio of 2 : 1, then the ratio of their masses will be Show Answer

Q224) Two circular copper discs A and B have the same thickness. If the diameter of A is twice that of B, the ratio of the moments of Inertias of A and B is Show Answer

Q225) The diameter of a thin circular disc of mass 2 kg is 0.2 m. Its moment of inertia about an axis passing through the edge and perpendicular to the plane of the disc is Show Answer

Q226) The radius of gyration of a disc of mass 100 gram and radius 5 cm about an axis passing through its centre of gravity and perpendicular to the plane is Show Answer

Q227) The moment of inertia of a ring of mass 5 gram and radius 1 cm about an axis passing through its edge and parallel to its natural axis is Show Answer

Q228) The M.I. of a solid cylinder of mass M and radius R about a line parallel to the axis of the cylinder and lying on the surface of the cylinder is Show Answer

Q229) The moment of inertia of a metre scale of mass 0.6 kg about an axis perpendicular to the scale and passing through 30 cm position on the scale is given by (Breadth of the scale is negligible) Show Answer

Q230) A wire of length L and mass M is bent in the form of a circular ring. Its moment of inertia about its axis is Show Answer

Q231) Two solid spheres are made of the same material. The ratio of their diameters is 2: 1. The ratio of their moments of inertia about their respective diameters is Show Answer

Q232) The ratio of the radii of gyration of a circular disc and a circular ring of the same radii and same mass about a tangential axis perpendicular to plane of disc or ring is Show Answer

Q233) Two identical concentric rings each of mass m and radius R are placed perpendicularly. What is the moment of inertia of the system about the axis of one of the rings? Show Answer

Q234) The M.I. of a solid sphere about its diameter is I. It is then casted into 8 small identical spheres. What is the M.I. of each small sphere about its diameter? Show Answer

Q235) What is the M.I. of a thin rod of length L and mass M about an axis passing through a point midway between the centre and the edge and perpendicular to its length? Show Answer

Q236) The M.I. of a uniform disc about a diameter is I. Its M.I. about an axis perpendicular to its plane and passing through a point on its rim is Show Answer

Q237) Moment of inertia of a ring of mass m = 3g and radius r = 1 cm about an axis passing through its edge and parallel to its natural axis is Show Answer

Q238) One quarter sector is cut from a uniform disc of radius R. This sector has mass M. It is made to rotate about a line perpendicular to its plane and passing through the centre of the original disc. What is its moment of inertia about the axis of rotation? Show Answer

Q239) What is the moment of inertia of a circular wire of mass M and radius R about its diameter? Show Answer

Q240) A solid cylinder has mass 'M', radius 'R' and length 'l'. Its moment of inertia about an axis passing through its centre and perpendicular to its own axis is Show Answer

Q241) The moment of inertia of a thin circular disc of mass M and radius R about any diameter is Show Answer

Q242) A circular disc of mass M and radius R is suspended from a nail in the wall. The nail is fixed very near to the rim of the disc. The moment of inertia of the disc about an axis along the nail is Show Answer

Q243) The radius of gyration of a body about an axis at a distance of 6 cm from the centre of mass is 10 cm. What is its radius of gyration about a parallel axis through its centre of mass? Show Answer

Q244) The ratio of the radii of gyration of a circular disc and of a circular ring of the same radius, about a tangential axis in the plane of the disc and the ring is Show Answer

Q245) Two rings have the same mass (m) and radius (r). They are placed in such away that their centres are at a common point and their planes are perpendicular to each other. What is the moment of inertia of the system about an axis passing through their centre and perpendicular to the plane of one of the ring? Show Answer

Q246) The M.I. of a uniform semicircular disc of mass M and radius R about a line perpendicular to the plane of the disc and passing through the centre is Show Answer

Q247) Two spheres of equal masses, one of which is a thin spherical shell and the other a solid, have the same moment of inertia about their respective diameters. What is the ratio of their radii? Show Answer

Q248) Two circular rings A and B of radii n R and R are made from the same wire. The M.I. of A about an axis passing through the centre and perpendicular to the plane of A is 27 times that of the smaller loop B. What is the value of n if the length of A = n (length of B)? Show Answer

Q249) Bodies of regular geometrical shape were allowed to roll on a horizontal surface. It was found that for one rolling body the translational K.E. was equal to rotational K.E. the body must be Show Answer

Q250) The moment of inertia of a thin uniform rod of mass M and length L, about an axis passing through a point midway between the centre and one end, perpendicular to its length is Show Answer

Q251) Let I be the moment of inertia of a uniform square plate about an axis AB that passes through its centre and is parallel to two of its sides. CD is a line in the plane of the plate that passes through the centre of the plate and makes an angle theta with AB. What is the moment of inertia of the plate about the axis CD? Show Answer

Q252) A thin uniform rod of length l and mass m is swinging freely about a horizontal axis passing through its end. Its maximum angular speed is omega. Its centre of mass rises to a maximum height of Show Answer

Q253) The M.I. of a hollow sphere of mass M and inner and outer radii R and 2R about its diameter is Show Answer

Q254) The moment of inertia of a disc about an axis which is tangential and parallel to its plane is I. Then, the moment of inertia of the same disc about an axis tangential but perpendicular to its plane will be Show Answer

Q255) When a torque acting on a system is increased, then which one of the following quantities will increase? Show Answer

Q256) A disc of mass 4 kg and radius 0.2 m, makes 20 rev/s, about an axis passing through its centre and perpendicular to the plane of the disc. The angular momentum of the disc is approximately equal to Show Answer

Q257) A body of mass 2 kg is rotating on a circular path of radius 0.5 m, with an angular velocity of 20 rad/s. If the radius of the path is doubled, then the new angular velocity will be Show Answer

Q258) A circular disc rotates about an axis passing through its centre with a certain angular velocity. Suddenly a small piece of the disc is broken from the edge and falls down. Then Show Answer

Q259) A body of mass m and radius of gyration K has an angular momentum L. Then its angular velocity is Show Answer

Q260) A man standing on a rotating horizontal circular table, suddenly sits down. What is conserved in this process? Show Answer

Q261) A particle performs a uniform circular motion with angular momentum L. If its angular frequency is halved and the rotational kinetic energy is doubled, then the new angular momentum will be Show Answer

Q262) A car of mass 1200 kg is travelling around a circular path of radius 250 m with a steady speed of 72 km/hour. What is its angular momentum? Show Answer

Q263) A uniform metre scale of mass 0.2 kg is rotated about an axis passing through its one end and perpendicular to its length at the rate of 60 revolutions/minute. What is its angular momentum? Show Answer

Q264) A swimmer while jumping into water from a height easily forms a loop in the air if Show Answer

Q265) A ballet dancer revolved at 24 r.p.m. with her hands folded. If she stretches her hands so that her M.I. increases by 20%, then the new frequency of rotation will be Show Answer

Q266) A solid sphere is rotating in a free space. If the radius of the sphere is increased, keeping the mass same, which one of the following will not be affected? Show Answer

Q267) A man, with outstretched arms, is spinning on a rotating table. He suddenly brings his arms down close to his sides. Which one of the following is true about his kinetic energy K and angular momentum L? Show Answer

Q268) r denotes the distance between the sun and the earth. Assume that the earth moves around the sun in a circular orbit of radius r. The angular momentum of the earth around the sun is proportional to Show Answer

Q269) A thin horizontal circular disc is rotating about a vertical axis passing through its centre. An insect is at rest at a point near the rim of the disc. The insect now moves along a diameter of the disc to reach its other end. During the journey of the insect, the angular speed of the disc Show Answer

Q270) A particle undergoes uniform circular motion. About which point on the plane of the circle, will the angular momentum of the particle remain constant? Show Answer

Q271) A uniform metallic rod rotates about its perpendicular bisector with constant angular speed. If it is heated uniformly to raise its temperature slightly Show Answer

Q272) By keeping the moment of inertia of a rotating body constant, if we double the time period, then the angular momentum of the body Show Answer

Q273) If the earth shrinks to half of its radius without change of mass, then the duration of the day will be Show Answer

Q274) A ball is confined to move along a circular path with decreasing speed. Then Show Answer

Q275) Angular momentum of a particle rotating with a central force is constant due to Show Answer

Q276) A particle of mass m is moving with a constant velocity along a line parallel to the +ve direction of the X-axis. The magnitude of its angular momentum w.r.t. the origin Show Answer

Q277) If all the ice on the polar caps of the earth melts, due to global warming then the duration of the day will be Show Answer

Q278) A one kg stone attached to the end of a 60 cm chain is revolving at the rate of 3 revolutions/second. It is found that after 30 second, it makes only one revolution per second. What is the mean torque? Show Answer

Q279) If the earth suddenly contracts to one third of its present size without any change in its mass, the ratio of the kinetic energies of the earth after and before contraction will be Show Answer

Q280) If the mass of the earth is kept constant and its radius is made half, then the duration of the day will be Show Answer

Q281) A uniform horizontal circular platform of mass 200 kg is rotating at 10 rpm about a vertical axis passing through its centre. A boy of mass 50 kg is standing on its edge. If the boy moves to the centre of the platform, the frequency of rotation would be Show Answer

Q282) A solid sphere rolls down a smooth inclined plane of height h. If it starts from rest then the speed of the sphere when it reaches the bottom is given by Show Answer

Q283) A sphere of moment of inertia I rolls down a smooth inclined plane. The ratio of its translation K.E. to the total energy is Show Answer

Q284) A disc at rest, gets an angular velocity of 40 rad/s, in 5 second, under constant angular acceleration. Through what angle the disc is turned during this time? Show Answer

Q285) A solid cylinder of mass 1 kg and radius 0.02 m, is rolling on a smooth horizontal surface with a uniform velocity of 0.1 m/s. Its total energy is Show Answer

Q286) A sphere is rolling on a horizontal surface without slipping. The ratio of the rotational K.E. to the total kinetic energy of the sphere is Show Answer

Q287) A body of radius R rolls without slipping. The radius of gyration of the body about an axis passing through its centre of mass is K. What is the fraction of total energy associated with its rotational energy? Show Answer

Q288) Two bodies of masses of 2 kg and 4 kg are moving with velocities of 2 m/s and 10 m/s towards each other under mutual gravitational attraction. What is the velocity of their centre of mass? Show Answer

Q289) The centre of mass of a system of two particles divides the distance between them Show Answer

Q290) A disc of mass 4.8 kg and radius 1 m is rolling on a horizontal surface without sliding with angular velocity of 600 rotations/min. What is the total kinetic energy of the disc? Show Answer

Q291) Four particles, each of mass 1 kg are placed at the corners of a square OABC of side 1 m. O is at the origin of the co-ordinate system. OA and OC are aligned along positive X-axis and positive Y-axis respectively. What is the position vector of their centre of mass? Show Answer

Q292) What is the total energy of a rolling ring of mass m and radius R? Show Answer

Q293) A body is rolling without slipping on a horizontal surface and its rotational kinetic energy is equal to its translational kinetic energy. The body is a Show Answer

Q294) What is the ratio of the rolling kinetic energy and rotational kinetic energy in the motion of a disc? Show Answer

Q295) Two particles A and B are at rest. They move towards each other under their mutual force of attraction. At the instant when the speed of A is v and the speed of B is 2v, the speed of the centre of mass of the system is Show Answer

Q296) At any instant, a rolling body may be considered to be in pure rotation about an axis passing through the point of contact. This axis is translating forward with a speed Show Answer

Q297) Three identical spheres each of mass 1 kg are placed touching one another with their centres in a straight line. Their centres are marked as A, B, C respectively. The distance of the centre of mass of the system from A is Show Answer

Q298) A solid sphere, a hollow sphere and a disc are released from the top of a frictionless inclined plane so that they slide down the inclined plane (without rolling). The maximum acceleration down the plane is Show Answer

Q299) Four point masses P, Q, R and S with respective masses 1 kg, 1 kg, 2 kg and 2 kg form the corners of a square of side a. The centre of mass of the system will be farthest from Show Answer

Q300) Two wheels of radii 10 cm and 30 cm are connected to each other by a belt. What is the ratio of the moment of inertia of the larger wheel to that of the smaller wheel, when both of them have the same angular momentum? Show Answer

Q301) Two spheres of unequal masses but of the same radii are released from the top of a smooth inclined plane. They roll down the plane without slipping. Which one will reach the bottom first? Show Answer

Q302) A uniform solid sphere and a disc of the same mass and of the same radius roll down a smooth inclined plane. They start from the top. What is the ratio of the times taken by them, to reach the bottom of the inclined plane? Show Answer

Q303) Two solid cylinders P and Q of the same mass and same radius start rolling down a fixed inclined plane from the same height at the same time. Cylinder P has most of its mass concentrated near its surface, while Q has most of its mass concentrated near the axis. Which statement(s) is (are) correct? Show Answer

Q304) A solid sphere, a disc and a solid cylinder all of the same mass and made of the same material are allowed to roll down (from rest) from the top of an inclined plane, then Show Answer

Q305) The kinetic energy of a rotating body depends upon the Show Answer

Q306) A ring and a disc roll on the horizontal surface without slipping with the same linear velocity. If both of them have the same mass and the total kinetic energy of the ring is 4 J then the total kinetic energy of the disc is Show Answer

Q307) Let 'M' be the mass and 'L' be the length of a thin uniform rod. In first case, the axis of rotation is passing through the centre and perpendicular to the length of the rod. In second case the axis of rotation is passing through one end and perpendicular to the length of the rod. The ratio of radius of gyration in first case to second case is Show Answer

Q308) A solid sphere of mass 2 kg is rolling on a frictionless horizontal surface with velocity 6 m/s. It collides on the free end of an ideal spring whose other end is fixed. The maximum compression produced in the spring will be (force constant of the spring = 36 N/m) Show Answer

Q309) A flywheel at rest is to reach an angular velocity of 24 rad/s in 8 second with constant angular acceleration. The total angle turned through during this interval is Show Answer