Centre of mass & RM

An energy of 484 J is spent in increasing the speed of a flywheel from 60 rpm to 360 rpm. The moment of inertia of the flywheel is :

• 0.7

• 0.07

• 3.22

• 30.8

Two objects of mass 10 kg and 20 kg respectively are connected to the two ends of a rigid rod of length 10 m with negligible mass. The distance of the center of mass of the system from the 10 kg mass is

• 10/3

• 20/3

• 10

• 5

Two particles of mass 5 kg and 10 kg respectively are attached to the two ends of a rigid rod of length 1 m with negligible mass.The centre of mass of the system from the 5 kg particle is nearly at a distance of :

• 50cm

• 67cm

• 80cm

• 33cm

Which of the following statements are correct ?

• (1)   Centre of mass of a body always coincides with the centre of gravity of the body.

• (2)   Centre of mass of a body is the point at which the total gravitational torque on the body is zero.

• (3)   A couple on a body produces both translational and rotational motion in a body(

• 4)   Mechanical advantage greater than one means that small effort can be used to lift a large load.

A circular platform is mounted on a frictionless vertical axle. Its radius R = 2 m and its moment of inertia about the axle is 200 kg m². It is initially at rest. A 50 kg man stands on the edge of the platform and begins to walk along the edge at the speed of 1 ms⁻¹ relative to the ground. Time taken by the man to complete one revolution is

• π

• 3π/2

• 2π

• π/2

Three masses are placed on the x-axis : 300 g at origin, 500 g at x = 40 cm and 400 g at x = 70cm. The distance of the centre of mass from the orgin is

• 40

• 45

• 50

• 30

Two persons of masses 55 kg and 65 kg respectively, are at the opposite ends of a boat. The length of the boat is 3.0 m and weights 100 kg. The 55 kg man walks up to the 65 kg man and sits with him. If the boat is in still water the centre of mass of the system shifts by

• 3m

• 2.3m

• 0

• 0.75m

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

• 2v

• zero

• 1.5v

• v

Consider a system of two particles having masses m₁ and m₂. If the particle of mass m₁ is pushed towards the mass centre of particles through a distance d. by what distance would be particle of mass m₂ move so as to keep the mass centre of particles at the original position ?

• m₁d/m₁+m₂

• m₁d/m₂

• d

• m₂/m₁

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

• √2gh

• √3gh/4

• √4gh/3

• √4gh