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 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 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. \(\frac{1}{2}m^2v^2\)

A vertical spring with a force constant \(k\) is fixed on a table. A ball of mass \(m\) at a height \(h\) above the free upper end of the spring falls vertically on the spring so that the spring is compressed by a distance \(d\). The net work done in the process is:
1. \(mg(h+d)+\frac{1}{2}kd^2\)
2. \(mg(h+d)-\frac{1}{2}kd^2\)
3. \(mg(h-d)-\frac{1}{2}kd^2\)
4. \(mg(h-d)+\frac{1}{2}kd^2\)

The potential energy of a long spring when stretched by \(2\) cm is \(U\). If the spring is stretched by \(8\) cm, the potential energy stored in it is:
1. \(4U\)
2. \(8U\)
3. \(16U\)
4. \(U/4\)

\(300 ~\text{J}\) of work is done in sliding a \(2~\text{kg}\) block up an inclined plane of height \(10~\text{m}\). Taking \(g=\) \(10\) m/s², work done against friction is:
1. \(200 ~\text{J}\)
2. \(100 ~\text{J}\)
3. \(\text{zero}\)
4. \(1000 ~\text{J}\)

When an object is shot from the bottom of a long, smooth inclined plane kept at an angle of \(60^\circ\) $$with horizontal, it can travel a distance \(x_1\) along the plane. But when the inclination is decreased to \(30^\circ\) $$and the same object is shot with the same velocity, it can travel \(x_2\) distance. Then \(x_1:x_2\) will be:
1. \(1:2\sqrt{3}\)
2. \(1:\sqrt{2}\)
3. \(\sqrt{2}:1\)
4. \(1:\sqrt{3}\)