Practice Test

Q1) The moment of inertia of a ring about a tangent to the circle of the ring is Show Answer

Q2) The angular acceleration assuming it to be uniform is Show Answer

Q3) How many revolutions does the engine make in 16 s. Show Answer

Q4) What is the angular acceleration of the wheel? Show Answer

Q5) The kinetic energy of the wheel, when 2 m of the cord has been pulled is Show Answer

Q6) Three bodies, a ring, a solid cylinder and a solid sphere roll down the same inclined plane without slipping. They start from rest. The radii of the bodies are identical. What is the velocity of the body that reaches down with the maximum velocity Show Answer

Q7) The moment of inertia of a solid sphere about a tangent to the sphere, given the mass of the sphere is M and its radius is R, is Show Answer

Q8) The moment of inertia of a disc of mass M and radius R about an axis normal to the disc and passing through a point on its edge is Show Answer

Q9) A child stands at the centre of a turntable with his two arms outstretched. The turntable is set rotating with an angular speed of 40 rev/min. How much is the angular speed of the child if he holds his hands back and thereby reduces moment of inertia of the system Show Answer

Q10) From a uniform disc of radius R, a circular hole of R/2 is cut out. The centre of the hole is R/2 from the centre of the original disc. The centre of gravity of the resulting body is at d from the centre of original disc opposite to the centre of cut portion d equals Show Answer

Q11) A meter stick is balanced on a knife edge at its centre. When two coins, each of mass 5 g are put on top of the other at the 12 cm mark, the stick is found to be balanced at 45 cm. The mass of the meter stick is Show Answer

Q12) A hoop of radius 2 m weighs 100 kg. It rolls along a horizontal floor so that its centre of mass has a speed of 20 cm/s. How much work has to be done to stop it? Show Answer

Q13) How far does the cylinder go up the plane? Show Answer

Q14) How long does the cylinder take to return to the bottom? Show Answer

Q15) A ring of mass 10 kg and diameter 0.4 m is rotated about its axis. If it makes 2100 revolutions per minute, then its angular momentum will be Show Answer

Q16) For the same total mass, which of the following will have the largest moment of inertia about an axis passing through the centre of gravity and perpendicular to the plane of body? Show Answer

Q17) Radius of gyration of a body about an axis at a distance of 6 cm from its centre of mass is 10 cm. The radius of gyration about a parallel axis through its centre of mass is Show Answer

Q18) Without weighing, how will you distinguish between the two identical balls of same material, but one being solid and the other one being hollow? Show Answer

Q19) A nearly mass less rod is pivoted at one end so that it can swing freely as a pendulum. Two masses 2 m and m are attached to it at distances b and 3 b respectively from the pivot. The rod is held horizontal and then released. The angular acceleration of the rod at the instant it is released is Show Answer

Q20) A body rolls down an inclined plane. If its kinetic energy of rotational motion is 40% of its kinetic energy of translation then the body is Show Answer

Q21) A paticle performs uniform circular motion with an angular momentum L. If the frequency of particle's motion is doubled and its kinetic energy is halved, then the angular momentum becomes Show Answer

Q22) The radius of gyration of a circular plate of radius R, about an axis perpendicular to its plane and bisecting a radius is Show Answer

Q23) Four particles, each of mass m, are placed symmetrically on the rim of a disc of mass M and radius R. The moment of inertia of this system about an axis passing through one of the particles and perpendicular to the plane of the disc is Show Answer

Q24) Frictional force on the cylinder is Show Answer

Q25) Acceleration of the cylinder is Show Answer

Q26) Angular acceleration of the cylinder is Show Answer

Q27) If the Earth shrinks to half the present radius, without any change in mass, then the duration of day and night becomes Show Answer

Q28) Which of the following has the highest moment of inertia when each of them has the same mass and the same radius? Show Answer

Q29) A uniform plane sheet of metal in the form of a triangle ABC has BC > A B > AC. Its moment of inertia will be smallest Show Answer

Q30) A closed tube, partly filled with a liquid and set horizontal, is rotated about a vertical axis passing through its centre. In the process, the moment of inertia of the system about its axis would Show Answer

Q31) A solid sphere, a spherical shell, a disc and a ring of the same radius are allowed to roll down an inclined plane simultaneously from the same height without slipping. Of these, the one which reaches the bottom first is Show Answer

Q32) The ratio of the time taken by a uniform solid sphere and a disc of the same mass and diameter to roll down from rest the same distance on an inclined plane is Show Answer

Q33) If the Earth is treated as a sphere of radius R and mass M, its angular momentum about the axis of its diurnal rotation with period T is Show Answer

Q34) A rigid spherical body is spinning around an axis without any external torque. Due to change in temperature, the volume increases by 1%. The angular speed will approximately Show Answer

Q35) A wheel of radius r and mass m stands in front of a step of height h. The least horizontal force which should be applied to the axle of the wheel to allow it to raise on the step is Show Answer

Q36) A recording disc rotates steadily at 45 rev/min on a table. When a small mass of 0.02 kg is dropped gently on the disc at a distance of 0.04 m from its axis and sticks to the disc, the rate of revolution falls to 36 rev/min. The moment of inertia of the disc about its centre is Show Answer

Q37) Statement 1 : Angular velocity is characteristic of a rigid body as a whole.
Statement 2 : Angular velocity may be different for different particles of rigid body about axis of rotation. Show Answer

Q38) Acceleration of plank is Show Answer

Q39) Find coefficient of friction just needed to have sphere rolling on plank Show Answer

Q40) Tension in string is Show Answer

Q41) Two blocks of masses 10 kg and 30 kg are placed on the same straight line with coordinates (0, 0) cm and (x, 0) cm, respectively. The block of 10 kg is moved on the same line through a distance of 6 cm towards the other block. The distance through which the block of 30 kg must be moved to keep the position of centre of mass of the system unchanged is Show Answer

Q42) Angular momentum of a single particle moving with constant speed along circular path Show Answer

Q43) A thin circular ring of mass M and radius r is rotating about its axis with an angular speed ca Two particles having mass m each are now attached at diametrically opposite points. The angular speed of the ring will become Show Answer

Q44) The magnitude of torque on a particle of mass 1 kg is 2.5 N-m about the origin. If the force acting on it is 1 N and the distance of the particle from the origin is 5 m, then the angle between the force and the position vector is (in radian) Show Answer

Q45) A string is wound around a hollow cylinder of mass 5 kg and radius 0.5 m. If the string is now pulled with a horizontal force of 40 N and the cylinder is rolling without slipping on a horizontal surface (see figure), then the angular acceleration of the cylinder will be (Neglect the mass and thickness of the string) Show Answer

Q46) To mop-clean a floor, a cleaning machine presses a (circular mop of radius R vertically down with a total force F and rotates it with a constant angular speed about its axis. If the force F is distributed uniformly over the mop and if coefficient of friction between the mop and the floor is μ, the torque applied by the machine on the mop in (N-m) is Show Answer

Q47) A bob of mass m attached to an inextensible string of length l is suspended from a vertical support. The bob rotates in a horizontal circle with an angular speed co rad/s about the vertical support. About the point of suspension, Show Answer

Q48) 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

Q49) A thin uniform rod of length / and mass m is swinging freely about a horizontal axis passing through its end. Its maximum angular speed is a Its centre of mass rises to a maximum height of Show Answer

Q50) Angular momentum of the particle rotating with a central force is constant due to Show Answer

Q51) A solid sphere is rotating in free space. If the radius of the sphere is increased keeping mass same, which one of the following will not be affected? Show Answer

Q52) A particle performing uniform circular motion has angular momentum L. If its angular frequency is doubled and its kinetic energy halved, then the new angular momentum is Show Answer

Q53) Two identical particles move towards each other with velocity 2v and v, respectively. The velocity of centre of mass is Show Answer

Q54) A body of mass 2 kg moving with a speed of 4 m/s makes an elastic collision with another body at rest and continues to move in the original direction but with one-fourth of its initial speed. The speed of the two body centre of mass is x / 10 m/s. Then, the value of x is. Show Answer

Q55) A person of 80 kg mass is standing on the rim of a circular platform of mass 200 kg rotating about its axis at 5 rpm. The person now starts moving towards the centre of the platform. What will be the rotational speed (in rpm) of the platform when the person reaches its centre? Show Answer

Q56) The centre of mass of a solid hemisphere of radius 8 cm is x cm from the centre of the flat surface. Then, value of x is ....... Show Answer

Q57) A system consists of two identical spheres each of mass 1.5 kg and radius 50 cm at the end of light rod. The distance between the centres of the two spheres is 5 m. What will be the moment of inertia of the system about an axis perpendicular to the rod passing through its mid-point? Show Answer

Q58) Moment of inertia of a square plate of side / about the axis passing through one of the corner and perpendicular to the plane of square plate is given by Show Answer

Q59) Assertion A Moment of inertia of a circular disc of mass M and radius R about X, Y-axes (passing through its plane) and Z-axis which is perpendicular to its plane were found to be I, I, and I, respectively. The respective radii of gyration about all the three axes will be the same.
Reason R A rigid body making rotational motion has fixed mass and shape.
In the light of the above statements, choose the most appropriate answer from the options given below. Show Answer

Q60) Consider a uniform wire of mass M and length L. It is bent into a semicircle. Its moment of inertia about a line perpendicular to the plane of the wire passing through the centre is Show Answer

Q61) Four identical solid spheres each of mass m and radius a are placed with their centres on the four corners of a square of side b. The moment of inertia of the system about one side of square, where the axis of rotation is parallel to the plane of the square is Show Answer

Q62) The radius of gyration of a uniform rod of length l, 1 about an axis passing through a point l/4 away from the centre of the rod and perpendicular to it, is Show Answer

Q63) The moment of inertia of a solid sphere, about an axis parallel to its diameter and at a distance of x from it, is 'I(x)'. Which one of the graphs represents the variation of I(x) with x correctly? Show Answer

Q64) Let the moment of inertia of a hollow cylinder of length 30 cm (inner radius 10 cm and outer radius 20 cm) about its axis be I. The radius of a thin cylinder of the same mass such that its moment of inertia about its axis is also I, is Show Answer

Q65) A circular hole of radius R/4 is made in a thin uniform disc having mass M and radius R, as shown in figure. The moment of inertia of the remaining portion of the disc about an axis passing through the point O and Perpendicular to the plane of the disc is Show Answer

Q66) Four point masses, each of value m, are placed at the corners of a square ABCD of side l. The moment of inertia of this system about an axis passing through A and parallel to BD is Show Answer

Q67) The moment of inertia of uniform semi-circular disc of mass M and radius r about a line perpendicular to the plane of the disc through the centre is Show Answer

Q68) Moment of inertia of a circular wire of mass M and radius R about its diameter is Show Answer

Q69) Two discs of same mass and different radii are made of different materials such that their thicknesses are 1 cm and 0.5 cm respectively. The densities of materials are in the ratio 3:5. The moment of inertia of these discs respectively about their diameters will be in the ratio of x/6. The value of x is........... Show Answer

Q70) If a solid sphere of mass 5 kg and a disc of mass 4 kg have the same radius. Then, the ratio of moment of inertia of the disc about a tangent in its plane to the moment of inertia of the sphere about its tangent will be . The value of x is.............. Show Answer

Q71) A coin placed on a rotating table just slips when it is placed at a distance of 1 cm from the centre. If the angular velocity of the table in halved, it will just slip when placed at a distance of ...... from the centre Show Answer

Q72) A solid cylinder and a solid sphere, having same mass M and radius R, roll down the same inclined plane from top without slipping. They start from rest. The ratio of velocity of the solid cylinder to that of the solid sphere, with which they reach the ground, will be Show Answer

Q73) A solid spherical ball is rolling on a frictionless horizontal plane surface about its axis of symmetry. The ratio of rotational kinetic energy of the ball to its total kinetic energy is Show Answer

Q74) A fly wheel is accelerated uniformly from rest and rotates through 5 rad in the first second. The angle rotated by the fly wheel in the next second, will be Show Answer

Q75) Consider a situation in which a ring, a solid cylinder and a solid sphere roll down on the same inclined plane without slipping. Assume that they start rolling from rest and having identical diameter. The correct statement for this situation. Show Answer

Q76) A body rolls down an inclined plane without slipping. The kinetic energy of rotation is 50% of its translational kinetic energy. The body is Show Answer

Q77) A cord is wound round the circumference of wheel of radius r. The axis of the wheel is horizontal and the moment of inertia about it is I. A weight mg is attached to the cord at the end. The weight falls from rest. After falling through a distance b, the square of angular velocity of wheel will be Show Answer

Q78) A wheel is rotating freely with an angular speed con a shaft. The moment of inertia of the wheel is I and the moment of inertia of the shaft is negligible. Another wheel of moment of inertia 37 initially at rest is suddenly coupled to the same shaft. The resultant fractional loss in the kinetic energy of the system is Show Answer

Q79) A uniform sphere of mass 500 g rolls without slipping on a plane horizontal surface with its centre moving at a speed of 5.00 cm/s. Its kinetic energy is Show Answer

Q80) A wedge of mass M =4 m lies on a frictionless plane. A particle of mass m aproaches the wedge with speed v. There is no friction between the particle and the plane or between the particle and the wedge. The maximum height climbed by the particle on the wedge is given by Show Answer

Q81) A homogeneous solid cylindrical roller of radius R and mass m is pulled on a cricket pitch by a horizontal force. Assuming rolling without slipping, angular acceleration of the cylinder is Show Answer

Q82) A uniform solid cylindrical roller of mass m is being pulled on a horizontal surface with force F parallel to the surface and applied at its centre. If the acceleration of the cylinder is a and it is rolling without slipping then the value of F is Show Answer

Q83) A solid sphere, a hollow sphere and ha ring are released from top of an inclined plane (frictionless), so that they slide down the plane. Then, maximum acceleration down the plane is for (no rolling) Show Answer

Q84) For a rolling spherical shell, the ratio of rotational kinetic energy and total kinetic energy is x / 5. The value of x is........ Show Answer

Q85) A solid sphere is rolling on a horizontal plane without slipping. If the ratio of angular momentum about axis of rotation of the sphere to the total energy of moving sphere is π:22 then, the value of its angular speed will be ....... rad/s Show Answer

Q86) A circular plate is rotating in horizontal plane, about an axis passing through its centre and perpendicular to the plate, with an angular velocity a A person sits at the centre having two dumbbells in his hands, the moment of inertia of the system become triple. If E be the initial kinetic energy of the system, then final kinetic energy will be E/x. The value of x is Show Answer

Q87) A body rotating with an angular speed of 600 rpm is uniformly accelerated to 1800 rpm in 10 s. The number of rotations made in the process is .... Show Answer

Q88) The angular speed of truck wheel is increased from 900 rpm to 2460 rpm in 26 s. The number of revolutions by the truck engine during this time is
(Assuming the acceleration to be uniform). Show Answer