A force \(F\) acting on an object varies with distance \(x\) as shown below:

The force is in Newton and \(x\) is in meters. The work done by the force in moving the object from \(x = 0\) to \(x = 6\) m is:

1.	\(18.0\) J	2.	\(13.5\) J
3.	\(4.5\) J	4.	\(9.0\) J

When a spring is subjected to 4 N force, its length is a metre and if 5 N is applied, its length is b metre. If 9 N is applied, its length will be:

1.  4b – 3a

2.  5b – a

3.  5b – 4a

4.  5b – 2a

The kinetic energy of a body is increased by 21%. The percentage increase in the magnitude of linear momentum of the body will be:

1.  10%

2.  20%

3.  Zero

4.  11.5%

The bob of a simple pendulum having length \(l,\) is displaced from the mean position to an angular position \(\theta\) with respect to vertical. If it is released, then the velocity of the bob at the lowest position will be:

1. \(\sqrt{2 g l \left(\right. 1 - \cos \theta \left.\right)}\)
2. \(\sqrt{2 g l \left(\right. 1 + \cos\theta)}\)
3. \(\sqrt{2 g l\cos\theta}\)
4. \(\sqrt{2 g l}\)

Water falls from a height of 60 m at the rate of 15 kg/s to operate a turbine. The losses due to frictional force are 10% of the input energy. How much power is generated by the turbine? $\left(g=10\right)$ $m/s^2$

A stone is dropped from a height \(h.\) It hits the ground with a certain momentum \(p.\) If the same stone is dropped from a height \(100\%\) more than the previous height, the momentum when it hits the ground will change by:
1. \(41\%\)
2. \(200\%\)
3. \(100\%\)
4.  \(68\%\)

A car of mass m starts from rest and accelerates so that the instantaneous power delivered to the car has a constant magnitude \(P_0\). The instantaneous velocity of this car is proportional to:
1.  \(t^{\frac{1}{2}}\)
2.  \(t^{\frac{-1}{2}}\)
3. \(\frac{t}{\sqrt{m}}\)
4. \(t^2 P_0\)

__________ of a two-particle system depends only on the separation between the two particles. The most appropriate choice for the blank space in the above sentence is:
1. kinetic energy
2. total mechanical energy
3. potential energy
4. total energy

The total work done on a particle is equal to the change in its kinetic energy: