A body of mass (\(4m\)) is lying in the x-y plane at rest. It suddenly explodes into three pieces. Two pieces, each of mass (\(m\)) move perpendicular to each other with equal speeds (\(u\)). The total kinetic energy generated due to explosion is:
1. | \(mu^2\) | 2. | \(1.5~mu^2\) |
3. | \(2~mu^2\) | 4. | \(3~mu^2\) |
A uniform force of \((3 \hat{i} + \hat{j})\) newton acts on a particle of mass \(2\) kg. Hence the particle is displaced from position \((2 \hat{i} + \hat{k})\) meter to position \((4 \hat{i} + 3 \hat{j} - \hat{k})\) meter. The work done by the force on the particle is:
1. | \(6\) J | 2. | \(13\) J |
3. | \(15\) J | 4. | \(9\) J |
The potential energy of a particle in a force field is \(U=\) where \(A\) and \(B\) are positive constants and \(r\) is the distance of the particle from the center of the field. For stable equilibrium, the distance of the particle is:
1. | \(\frac{B}{A}\) | 2. | \(\frac{B}{2A}\) |
3. | \(\frac{2A}{B}\) | 4. | \(\frac{A}{B}\) |
1. | \(B\). | same as that of
2. | \(B\). | opposite to that of
3. | \(\theta = \text{tan}^{-1}\left(\frac{1}{2} \right)\) to the positive \(x\)-axis. |
4. | \(\theta = \text{tan}^{-1}\left(\frac{-1}{2} \right )\) to the positive \(x\)-axis. |
The potential energy of a system increases if work is done:
1. | by the system against a conservative force |
2. | by the system against a non-conservative force |
3. | upon the system by a conservative force |
4. | upon the system by a non-conservative force |
Force \(F\) on a particle moving in a straight line varies with distance \(d\) as shown in the figure. The work done on the particle during its displacement of \(12\) m is:
1. \(21\) J
2. \(26\) J
3. \(13\) J
4. \(18\) J
A ball moving with velocity 2 ms-1 collides head-on with another stationary ball of double the mass. If the coefficient of restitution is 0.5, then their velocities (in ms-1) after the collision will be:
1. 0, 1
2. 1, 1
3. 1, 0.5
4. 0, 2
An engine pumps water through a hose pipe. Water passes through the pipe and leaves it with a velocity of 2 ms-1. The mass per unit length of water in the pipe is What is the power of the engine?
1. 400 W
2. 200 W
3. 100 W
4. 800 W
A body of mass \(1\) kg is thrown upwards with a velocity \(20\) ms-1. It momentarily comes to rest after attaining a height of \(18\) m. How much energy is lost due to air friction?
(Take \(g=10\) ms-2)
1. \(20\) J
2. \(30\) J
3. \(40\) J
4. \(10\) J