The law of conservation of angular momentum is valid when:
1. | The net force is zero and the net torque is non-zero | 2. | The net force is non-zero and the net torque is non zero |
3. | Net force may or may not be zero and net torque is zero | 4. | Both force and torque must be zero |
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:
1. | remain stationary |
2. | move up |
3. | move down |
4. | first moves up and then return to its initial position |
Two loads \(P_1\) \(P_2\)\((P_1>P_2)\) 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. | \(\left(\frac{(P_1-P_2)^{\frac{1}{2}}}{P_1+P_2}\right)g\) | 2. | \(\left(\frac{P_1-P_2}{P_1+P_2}\right)g\) |
3. | \(\left( \frac{P_1-P_2}{P_1+P_2}\right)^2g\) | 4. | \(\left( \frac{P_1+P_2}{P_1-P_2}\right)g\) |
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. | \(2 \mathrm{V}_0 / 5 \mathrm{L}\) |
A particle rotating on a circular path of the radius \(\frac{4}{\pi}~\text{m}\) 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
1. | \(2ml^2\) | 2. | \(4ml^2\) |
3. | \(3ml^2\) | 4. | \(ml^2\) |
The mass per unit length of a non-uniform rod of length \(L\) is given by \(\mu =λx^{2}\) where \(\lambda\) 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. | \(\frac{L}{2}\) | 2. | \(\frac{L}{4}\) |
3. | \(\frac{3L}{4}\) | 4. | \(\frac{L}{3}\) |
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 centre of mass of the system (in SI units) 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. \(OF\)
A bomb is projected from the ground at a horizontal range of \(R\). If the bomb explodes mid-air, then the range of its centre of mass is:
1. \(\frac{R}{2}\)
2. \(R\)
3. \(2R\)
4. \(\frac{2R}{3}\)