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
An engine pumps water continuously through a hose. Water leaves the hose with a velocity \(v\) and \(m\) is the mass per unit length of the water jet. What is the rate at which kinetic energy is imparted to water?
1. \(\frac{1}{2}mv^3\)
2. \(mv^3\)
3. \(\frac{1}{2}mv^2\)
4. \(\frac{1}{2}m^2v^2\)