The work done in increasing the length of a massless spring from its natural length 15 cm to 15.1 cm is 20 J. Work done in increasing the length from 15.1 cm to 15.2 cm will be:

1.	20 J	2.	40 J
3.	60 J	4.	80 J

A body of mass m moving at a certain speed suffers a perfectly inelastic collision with a body of mass M at rest. The ratio of the final kinetic energy of the system to the initial kinetic energy will be:

1. \(m \over {m + M}\)

2. \(M \over {m + M}\)

3. \({m + M} \over m\)

4. \({m + M} \over M\)

An automobile of mass m accelerates from rest, while the engine supplies constant power P. The speed of the automobile as a function of time is given by:

1.  $\mathrm{v} = {\left(\frac{2\mathrm{Pt}}{\mathrm{m}}\right)}^{1/2}$

2.  $\mathrm{v} = {\left(2\mathrm{Ptm}\right)}^{1/3}$

3.  $\mathrm{v} = {\left(\frac{8}{9}\frac{\mathrm{P}}{\mathrm{m}}{\mathrm{t}}^3\right)}^{1/2}$

4.  $\mathrm{v} = {\left(2{\mathrm{Pt}}^3\mathrm{m}\right)}^{1/2}$

The potential energy of a particle of mass 1 kg free to move along the X-axis is given by \(U(x) = (3x^2-4x+6)~\text{J}\). The force acting on the particle at x = 0 will be:

1.  2$\hat{\mathrm{i}}$ N

2.  -4$\hat{\mathrm{i}}$ N

3.  5$\hat{\mathrm{i}}$ N

4.  4$\hat{\mathrm{i}}$ N

Work done by frictional force during walking of a man is:

1.  Positive

2.  Negative

3.  Zero

4.  Maybe positive or negative

A particle is moving such that the potential energy U varies with position in metre as U (x) = ($4{\mathrm{x}}^2$ - 2x + 50) J. The particle will be in equilibrium at: 
1. x = 25 cm
2. x = 2.5 cm
3. x = 25 m
4. x = 2.5 m

Select the incorrect statement about potential energy:

1. A change in potential energy is equal to work done against the internal conservative force.

2. A change in potential energy is independent of the reference point.

3. A change in potential energy depends on the reference frame.

4. The potential energy at a point is not unique.

A block of mass m is moving with speed v towards a spring block system. If the collision is perfectly inelastic, then the maximum compression in the spring will be:

1.  $\mathrm{v}\sqrt{\frac{\mathrm{m}}{\mathrm{k}}}$

2.  $\mathrm{v}\sqrt{\frac{2\mathrm{m}}{\mathrm{k}}}$

3.  $\mathrm{m}\sqrt{\frac{\mathrm{v}}{2\mathrm{k}}}$

4.  $\mathrm{v}\sqrt{\frac{\mathrm{m}}{2\mathrm{k}}}$

The figure shows the potential energy function U of a system in which a particle is in one-dimensional motion. In which region is the magnitude of the force on the particle greatest? (x: position)

Which of the following is not a unit of energy?
1. watt-hour
2. joule
3. eV
4. N/m