System of Particles and Rotational Motion · Question 57

The moment of inertia of a thin uniform rod of mass M and length L about an axis passing through its midpoint and perpendicular to its length is I0. Its moment of inertia about an axis passing through one of its ends and perpendicular to its length is

1. I0 + ML2/2
2. I0 + ML2/4
3. I0 + 2ML2
4. I0 + ML2

From a circular disc of radius R and mass 9M, a small disc of mass M and radius R3 is removed concentrically. The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through its centre is

1. 409MR2
2. MR2
3. 4MR2
4. 49MR2

A solid cylinder and a hollow cylinder, both of the same mass and same external diameter are released from the same height at the same time on an inclined plane. Both roll down without slipping. Which one will reach the bottom first?

1. Both together only when angle of inclination of plane is 45
2. Both together
3. Hollow cylinder
4. Solid cylinder

A thin circular ring of mass M and radius r is rotating about its axis with constant angular velocity . Two objects each of mass m are attached gently to the opposite ends of a diameter of the ring. The ring now rotates with angular velocity given by

1. (M+2m) 2m
2. 2M M+2m
3. (M+2m) M
4. M M+2m

Which one of the following pairs of statements is correct ?

1. D and A only
2. A and B only
3. B and C only
4. C and D only

A circular disk of moment of inertia It is rotating in a horizontal plane, about its symmetry axis, with a constant angular speed i. Another disk of moment of inertia Ib is dropped coaxially onto the rotating disk. Initially the second disk has zero angular speed. Eventually both the disks rotate with a constant angular speed . The energy lost by the initially rotating disc to friction is

1. 12 Ib2(It + Ib) i2
2. 12 It2(It + Ib) i2
3. Ib - It(It + Ib) i2
4. 12 Ib It(It + Ib) i2

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 :

1. 2v
2. zero
3. 1.5 v
4. v

A thin circular ring of mass M and radius R is rotating in a horizontal plane about an axis vertical to its plane with a constant angular velocity . If two objects each of mass m be attached gently to the opposite ends of a diameter of the ring, the ring will then rotate with an angular velocity

1. MM+2m
2. (M+2m)M
3. MM+m
4. (M-2m)M+2m

If F is the force acting on a particle having position vector r and be the torque of this force about the origin, then

1. r > 0 and F < 0
2. r = 0 and F = 0
3. r = 0 and F 0
4. r 0 and F = 0

Four identical thin rods each of mass M and length l, form a square frame. Moment of inertia of this frame about an axis through the centre of the square and perpendicular to its plane is

1. 23Ml2
2. 133Ml2
3. 13Ml2
4. 43Ml2