At t = 0, the positions of the two blocks are shown. There is no external force acting on the system. Find the coordinates of the center of mass of the system at t = 3 seconds:
   

1.	(1, 0)	2.	(3, 0)
3.	(4.5, 0)	4.	(2.25, 0)

A uniform square plate ABCD has a mass of 10 kg. If two point masses of 5 kg each are placed at the corners C and D as shown in the adjoining figure, then the centre of mass shifts to the mid-point of:
          
1. OH

2. DH

3. OG

4. OF 

The mass per unit length of a non-uniform rod of length L is given by $\mathrm{\mu }={\mathrm{\lambda x}}^2$ where $\mathrm{\lambda }$ is a constant and x is the distance from one end of the rod. The distance between the centre of mass of the rod and this end is:

1. $\frac{\mathrm{L}}{2}$

2. $\frac{\mathrm{L}}{4}$

3. $\frac{3\mathrm{L}}{4}$

4. $\frac{\mathrm{L}}{3}$

Four-point masses each of value \(m\) are placed at the corners of a square ABCD of side \(l\). The moment of inertia of this system about an axis passing through A and parallel to BD will be:

A particle rotating on a circular path of the radius $\frac{4}{\mathrm{\pi }}\mathrm{m}$ at 300 rpm reaches 600 rpm in 6 revolutions. If the angular velocity increases at a constant rate, find the tangential acceleration of the particle.

1. 10 m/s²

2. 12.5 m/s²

3. 25 m/s²

4. 50 m/s²

The center of mass of a system of particles does not depend upon:

A particle is moving with a constant velocity along a line parallel to the positive x-axis. The magnitude of its angular momentum with respect to the origin is:

A rope is wrapped around a hollow cylinder with a mass of 3 kg and a radius of 40 cm. What is the angular acceleration of the cylinder if the rope is pulled with a force 30 N?

1. 0.25 rad s^–2 

2. 25 rad s^–2

3. 5 m s^–2 

4. 25 m s^–2

A rigid body rotates with an angular momentum of \(L.\) If its kinetic energy is halved, the angular momentum becomes:
1. \(L\)
2. \(L/2\)
3. \(2L\)
4. \(L/\)$\sqrt{2}$

A rod is falling down with constant velocity \(V_0\) as shown. It makes contact with hinge A and rotates around it. The angular velocity of the rod just after the moment when it comes in contact with hinge A is: