A uniform force of \((3 \hat{i} + \hat{j})\) newton acts on a particle of mass \(2~\text{kg}.\) Hence the particle is displaced from the position \((2 \hat{i} + \hat{k})\) metre to the position \((4 \hat{i} + 3 \hat{j} - \hat{k})\) metre. The work done by the force on the particle is:
1. \(6~\text{J}\)
2. \(13~\text{J}\)
3. \(15~\text{J}\)
4. \(9~\text{J}\)

The potential energy of a system increases if work is done:

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: 

              

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 $100$ $kg$ $m^{-1}.$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. \(\frac{1}{2}m^2v^2\)