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. $\frac{\mathrm{L}}{3}$

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 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:

Two loads ${\mathrm{P}}_1$ $\mathrm{and}$ ${\mathrm{P}}_2$ (${\mathrm{P}}_1$ $>{\mathrm{P}}_2$) are connected by a string passing over a fixed pulley. The center of gravity of loads are initially at the same height. Find the acceleration of the center of gravity of the system:
1. \(\left(\frac{(P_1-P_2)^{\frac{1}{2}}}{P_1+P_2}\right)\text{g}\)
2. \(\left(\frac{P_1-P_2}{P_1+P_2}\right)\text{g}\)
3. \(\left( \frac{P_1-P_2}{P_1+P_2}\right)^2 \text{g}\)
4. \(\left( \frac{P_1+P_2}{P_1-P_2}\right)\text{g}\)

A man hangs from a rope attached to a hot-air balloon. The man's mass is greater than the mass of the balloon and its contents. The system is stationary in the air. If the man now climbs up to the balloon using the rope, the centre of mass of the "man plus balloon" system will: