The ratio of the radii of gyration of a circular disc to that of a circular ring, each of the same mass and radius, around their respective axes is:

1.	\(\sqrt{3}:\sqrt{2}\)	2.	\(1:\sqrt{2}\)
3.	\(\sqrt{2}:1\)	4.	\(\sqrt{2}:\sqrt{3}\)

A thin rod of length \(L\) and mass \(M\) is bent at its midpoint into two halves so that the angle between them is \(90^{\circ}\). The moment of inertia of the bent rod about an axis passing through the bending point and perpendicular to the plane defined by the two halves of the rod is:
1.  \(\frac{ML^2}{24}\)
2.  \(\frac{ML^2}{12}\)
3.  \(\frac{ML^2}{6}\)
4.  \(\frac{\sqrt{2}ML^2}{24}\)

A wheel has an angular acceleration of \(3.0\) rad/s² and an initial angular speed of \(2.0\) rad/s. In a time of \(2\) s, it has rotated through an angle (in radians) of:

A uniform rod \(AB\) of length \(l\) and mass \(m\) is free to rotate about point \(A\). The rod is released from rest in the horizontal position. Given that the moment of inertia of the rod about \(A\) is \(\dfrac{ml^2}{3}\) the initial angular acceleration of the rod will be: 
       
1. \(\dfrac{2g}{3l}\)
2. \(\dfrac{mgl}{2}\)
3. \(\dfrac{3}{2}gl\)
4. \(\dfrac{3g}{2l}\)

A particle of mass \(m\) moves in the XY plane with a velocity \(v\) along the straight line AB. If the angular momentum of the particle with respect to the origin \(O\) is \(L_A\) when it is at \(A\) and \(L_B\) when it is at \(B,\) then: 
         

The moment of inertia of a uniform circular disc of radius \(R\) and mass \(M\) about an axis touching the disc at its diameter and normal to the disc is:
1. $M{R}^2$

2. $\frac{2}{5}M{R}^2$

3. $\frac{3}{2}M{R}^2$

4. $\frac{1}{2}M{R}^2$

A uniform rod of length \(l\) and mass \(M\) is free to rotate in a vertical plane about \(A\). The rod, initially in the horizontal position, is released. The initial angular acceleration of the rod is: (Moment of inertia of the rod about \(A\) is \(\frac{Ml^2}{3}\))
1. \(\frac{3g}{2l}\)
2. \(\frac{2l}{3g}\)
3. \(\frac{3g}{2l^2}\)
4. \(\frac{Mg}{2}\)

Two bodies of mass \(1\) kg and \(3\) kg have position vectors \(\hat{i}+2\hat{j}+\hat{k}\) and \(-3\hat{i}-2\hat{j}+\hat{k}\) respectively. The centre of mass of this system has a position vector:
1. \(-2\hat{i}+2\hat{k}\)
2. \(-2\hat{i}-\hat{j}+\hat{k}\)
3. \(2\hat{i}-\hat{j}-2\hat{k}\)
4. \(-\hat{i}+\hat{j}+\hat{k}\)

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 ω. If two objects each of mass m are attached gently to the opposite ends of the diameter of the ring, the ring will then rotate with an angular velocity: