Given below are two statements: 

Assertion (A):	Angular momentum of an isolated system of particles is conserved.
Reason (R):	The net torque on an isolated system of particles is zero and the rate of change of angular momentum equals the torque.

 

1.	Both (A) and (R) are True and (R) is the correct explanation of (A).
2.	Both (A) and (R) are True but (R) is not the correct explanation of (A).
3.	(A) is True but (R) is False.
4.	(A) is False but (R) is True.

The moment of inertia of a uniform square lamina, of mass \(m\), about one of its diagonals (diagonal-length: \(d\)) is:
1. \(\dfrac{md^2}{6}\)

2. \(\dfrac{md^2}{3}\)

3. \(\dfrac{md^2}{12}\)

4. \(\dfrac{md^2}{24}\)

A uniform solid wheel of mass \(m,\) radius \(R\) encounters a rectangular step of height \(h.\) The torque of the weight \(mg,\) of the wheel, about the forward edge of the step (\({A}\)) is (in magnitude):
                    
1. \(mgR\)
2. \(mg(R-h)\)
3. \(mgh\)
4. \(mg\)\(\sqrt{h(2R-h)}\)

The moment of inertia of a uniform rod of mass \(m\) and length \(L,\) about an axis passing through its centre and making an angle \(\theta\) with the rod is:
         

 

The center of mass of a thin conical surface of height \(h\) lies at a distance \(\lambda h\) from its apex, the base of the cone being hollow. The value of \(\lambda\) equals:

A uniform rod of mass \(m\) and length \(L\) is struck at both ends by two particles of masses m, each moving with identical speeds \(u,\) but in opposite directions, perpendicular to its length. The particles stick to the rod after colliding with it. The system rotates with an angular speed:

The moment of inertia of a uniform solid sphere of mass \(m\) and radius \(R\) about a diameter equals the moment of inertia of a solid uniform cylinder of radius \(r\) and height \(2r,\) about its axis. Their masses are the same. Then:
1. \(3r^{2}=4R^{2}\)
2. \(3r^{2}=2R^{2}\)
3. \(5r^{2}=2R^{2}\)
4. \(5r^{2}=4R^{2}\)

The centre-of-mass of a thin, uniform triangular lamina lies at its:

The centre-of-mass of a combination of a hemispherical shell and a cylindrical shell, both having the same height and radii and same mass, lies at a distance \(h\) from the centre of the hemisphere. Then, \(h\) equals: