System of Particles and Rotational Motion

A circular disc is to be made by using iron and aluminium so that it acquired maximum moment of inertia about geometrical axis. It is possible with

1. aluminium at interior and iron surround to it
2. iron at interior and aluminium surround to it
3. using iron and aluminium layers in alternate order
4. sheet of iron is used at both external surface and aluminium sheet as internal layers.

A disc is rolling, the velocity of its centre of mass is vcm. Which one will be correct?

1. the velocity of the highest point is 2vcm and of the point of contact is zero
2. the velocity of the highest point is vcm and of the point of contact is vcm
3. the velocity of the highest point is 2vcm and of the point of contact is vcm
4. the velocity of the highest point is 2vcm and of the point of contact is 2vcm.

For the adjoining diagram (a uniform right-angled triangular plate ABC), the correct relation between I1, I2 and I3 is (I – moment of inertia about the marked side) [figure]

1. I1 > I2
2. I2 > I1
3. I3 > I1
4. I3 > I2

For a hollow cylinder and a solid cylinder rolling without slipping on an inclined plane, then which of these reaches earlier

1. solid cylinder
2. hollow cylinder
3. both simultaneously
4. can't say anything