The moment of inertia of a uniform semicircular wire of mass \(\mathrm{M}\) and radius \(\mathrm{r}\) about a line perpendicular to the plane of the wire through the centre is:
1. \(\mathrm{Mr}^{2}\)

2. \(\frac{1}{2} \mathrm{Mr}^{2}\)

3. \(\frac{1}{4} \mathrm{Mr}^{2}\)

4. \(\frac{2}{5} \mathrm{Mr}^{2}\)

Let \(I_1\) and \(I_2\) be the moments of inertia of two bodies of identical geometrical shape, the first made of aluminium and the second of iron:

A body having its centre of mass at the origin has three of its particles at (a, 0, 0), (0, a, 0), (0, 0, a). The moments of inertia of the body about the X and Y axes are 0.20 kg-m² each. The moment of inertia about the Z-axis:

1. is 0.20 kg-m²

2. is 0.40 kg-m²

3. is \(0.20\sqrt2\) kg-m²

4. cannot be deduced with this information

A cubical block of mass M and edge a slides down a rough inclined plane of inclination θ with a uniform velocity. The torque of the normal force on the block about its centre has a magnitude

1. zero

2. Mga

3. Mga sin θ

4. \(\frac{1}{2}\) Mga sin θ

A thin circular ring of mass \(M\) and radius \(r\) is rotating about its axis with an angular speed \(\omega\). Two particles having mass \(m\) each are now attached at diametrically opposite points. The angular speed of the ring will become:
1. \(\frac{\omega M}{M+m}\)

2. \(\frac{\omega M}{M+2 m}\)

3. \(\frac{\omega(M-2 m)}{M+2 m}\)

4. \(\frac{\omega(M+2 m)}{M}\)

A person sitting firmly over a rotating stool has his arms stretched. If he folds his arms, his angular momentum about the axis of rotation:

The axis of rotation of a purely rotating body:

Choose the correct option:

Consider the following two equations
            (A) L = I ω    (B) \(\frac{dL}{dt}=\Gamma\)
In noninertial frames:

1. both A and B are true

2. A is true but B is false

3. B is true but A is false

4. both A and B are false

A particle moves on a straight line with a uniform velocity. Its angular momentum:

Choose the correct option:

If there is no external force acting on a non-rigid body which of the following quantities must remain constant?