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
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) |
The mass per unit length of a non-uniform rod of length L is given by where 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.
2.
3.
4.
The center of mass of a system of particles does not depend upon:
1. | position of particles |
2. | relative distance between particles |
3. | masses of particles |
4. | force acting on the particle |
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:
1. | zero |
2. | increasing with \(x\) |
3. | decreasing with \(x\) |
4. | remaining constant |
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. \(L/\)
A particle rotating on a circular path of the radius 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 coordinates of the centre of mass of a uniform plate of shape as shown in the figure are:
1. | \(\frac{L}{2}, \frac{L}{2} \) | 2. | \(\frac{5 L}{12}, \frac{5 L}{12} \) |
3. | \(\frac{5}{3} L, \frac{2}{3} L \) | 4. | \(\frac{3 L}{4}, \frac{L}{2}\) |
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:
1. | \(2 \mathrm{V}_0 / 3 \mathrm{L} \) | 2. | \(3 \mathrm{V}_0 / 2 \mathrm{L} \) |
3. | \(\mathrm{V}_0 / \mathrm{L} \) | 4. | \(2 \mathrm{V}_0 / 5 \mathrm{L}\) |
Two loads ( ) 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. \(\left( \frac{P_1+P_2}{P_1-P_2}\right)\text{g}\)