# System of Particles and Rotational Motion

SET – A

Q. 1 A circular ring and a circular disc of the same radius have the same moment of inertia about an axis passing through their centres and perpendicular to their planes. What is the ratio of their masses?

Q. 2 A planet revolves the sun under the effect of the gravitational force exerted by the sun. Why is the torque on the planet due to gravitational force zero? [ θ=0 Degree]

Q. 3 There are 100 passengers in a stationary railway compartment. A physical fight starts between the passengers over some difference of opinion. Will the position of the centre of mass of the compartment change ? Give reason. [Yes]

Will the position of CM of the system (compartment +100 passengers) change? Give reason.
[No, Because no External Torque is acting on the system]

Q.4 If the sun rotates around itself once in 27 days. if it expands to twice its present diameter, what would be its new period of revolution? [108 Days]

Q. 5 A solid sphere is rolling on a frictionless plane surface about its axis of symmetry. Find the ratio of its rotational kinetic energy to its total kinetic energy. [2:7]

Q.6 Discuss at least two examples angular momentum of the system remains constant.

Q. 7
Establish a relation between torque and moment of inertia. (2)

Q.8 Four particles of masses 2 kg, 3 kg, 1 kg and 6 Kg are respectively located at
the four corners A, B, C & D of a square of side 2 m. Calculate the moment of inertia of the system about
a) the side BC [32 Kg/m2]
b) the diagonal BD [16 Kg/m2]
c) an axis passing through the point of intersection of the diagonals and
perpendicular to the plane of the square. [24 Kg/m2]

Q.9 State perpendicular axis theorem. Derive an expression for the moment inertia of a circular disc (a) about an axis perpendicular to its plane (b) about a tangent in the plane. (5)

SET – B

Q.1 A boat likely to capsize if the person sitting in the boat stand up. Why? (1)

Q.2 The angular momentum of the wheel changes from 2L to 5L in 3 seconds. What is the magnitude of the torque acting on it? (1)

Q.3 Same as in the above set. (1)

Q.4 If earth shrinks suddenly to 1/27 of its original volume, what will be the duration of the day? (2)

Q.5 A 40 kg flywheel in the form of a uniform circular disc of 1 m radius is making 120 rpm (revolutions per minute). Calculate the angular momentum. (2)

Q.6 Discuss the motion of the centre of mass of an (i) firecracker that explodes in the air and (ii) the earth-moon system. (2)
[i) In absence of air drag the CM of the cracker would follow the same parabolic path until fragments hit the ground. ii) The common CM of the Earth-Moon System follows a elliptical path.

Q.7 Prove that the centre of mass of two particles divide the line joining the particles in the inverse ratio of their masses. [Prove that m1/m2=r1/r2 by taking CM at the origin.]

Q.8 Same as in the above set. (1)

Q.9 State parallel axis theorem. Derive an expression for the moment of inertia of a circular disc (a) about an axis perpendicular to its plane (b) about a tangent perpendicular to the plane. (5)