Systems of Particles and Rotational Motion Physics - Systems of Particles and Rotational Motion

The net external torque on a system of particles about an axis is zero. Which of the following are compatible with it?

1. The forces may be acting radially from a point on the axis.
2. The forces may be acting on the axis of rotation.
3. The forces may be acting parallel to the axis of rotation.
4. The torque caused by some forces may be equal and opposite to that caused by other forces.

For which of the following does the centre of mass lie outside the body?

1. A pencil
2. A shotput
3. A dice
4. A bangle

In problem 7.5, the CM of the plate is now in the following quadrant of x - y plane:

1. I
2. II
3. III
4. IV

The variation of angular position  of a point on a rotating rigid body, with time t is shown in is the body rotating clock-wise or anti-clockwise?

A door is hinged at one end and is free to rotate about a vertical axis. Does its weight cause any torque about this axis? Give reason for your answer.

The vector sum of a system of non-collinear forces acting on a rigid body is given to be non-zero. If the vector sum of all the torques due to the system of forces about a certain point is found to be zero, does this mean that it is necessarily zero about any arbitrary point?

The centre of gravity of a body on the earth coincides with its centre of mass for a ‘small’ object whereas for an ‘extended’ object it may not. What is the qualitative meaning of ‘small’ and ‘extended’ in this regard?
For which of the following the two coincides? A building, a pond, a lake, a mountain?

Why does a solid sphere have smaller moment of inertia than a hollow cylinder of same mass and radius, about an axis passing through their axes of symmetry?