Potential energy is defined:

1.	Only in conservative fields
2.	As the negative of the work done by conservative forces
3.	As the negative of the work done by external forces when \(\Delta K=0\)
4.	All of these

A stick of mass m and length l is pivoted at one end and is displaced through an angle $\mathrm{\theta }$. The increase in potential energy is 

1. $\mathrm{mg}\frac{\mathrm{l}}{2}(1-\mathrm{cos\theta })$

2. $\mathrm{mg}\frac{\mathrm{l}}{2}(1+\mathrm{cos\theta })$

3. $\mathrm{mg}\frac{\mathrm{l}}{2}(1-\mathrm{sin\theta })$

4. $\mathrm{mg}\frac{\mathrm{l}}{2}(1+\mathrm{sin\theta })$

A spring with spring constants k when compressed by 1 cm, the potential energy stored is U. If it is further compressed by 3 cm, then change in its potential energy is

1. 3U

2. 9U

3. 8U

4. 15U

Two springs have force constant K₁ and K₂ (K₁>K₂). Each spring is extended by same force F. If their elastic potential energy are E₁ and E₂ then $\frac{{\mathrm{E}}_1}{{\mathrm{E}}_2}$ is

1. $\frac{{\mathrm{K}}_1}{{\mathrm{K}}_2}$

2. $\frac{{\mathrm{K}}_2}{{\mathrm{K}}_1}$

3. $\sqrt{\frac{{\mathrm{K}}_1}{{\mathrm{K}}_2}}$

4. $\sqrt{\frac{{\mathrm{K}}_2}{{\mathrm{K}}_1}}$

Initially mass m is held such that spring is in relaxed condition. If mass m is suddenly released, maximum elongation in spring will be

1. $\frac{\mathrm{mg}}{\mathrm{k}}$

2. $\frac{2\mathrm{mg}}{\mathrm{k}}$

3. $\frac{\mathrm{mg}}{2\mathrm{k}}$

4. $\frac{\mathrm{mg}}{4\mathrm{k}}$

On a particle placed at origin a variable force $\mathrm{F}=-\mathrm{ax}$ (where a is a positive constant) is applied. If $\mathrm{U}\left(0\right)=0$, the graph between potential energy of particle U(x) and x is best represented by

1. 

2. 

3. 

4. 

The variation of potential energy U of a body moving along x-axis varies with its position (x) as shown in figure

The body is in equilibrium state at

1. A

2. B

3. C

4. Both A & C

A uniform chain of length L and mass M is lying on a smooth table and one third of its length is hanging vertically down over the edge of the table. If g is acceleration due to gravity, the minimum work required to pull the hanging part of the chain on the table is

1. MgL

2. $\frac{\mathrm{MgL}}{3}$

3. $\frac{\mathrm{MgL}}{9}$

4. $\frac{\mathrm{MgL}}{18}$

A block of mass m moving with velocity v₀ on a smooth horizontal surface hits the spring of constant k as shown. The maximum compression in spring is

1. $\sqrt{\frac{2\mathrm{m}}{\mathrm{k}}}.v_0$

2. $\sqrt{\frac{\mathrm{m}}{\mathrm{k}}}.v_0$

3. $\sqrt{\frac{\mathrm{m}}{2\mathrm{k}}}.v_0$

4. $\frac{\mathrm{m}}{2\mathrm{k}}.v_0$

For a particle moving under the action of a variable force, kinetic energy-position graph is given, then

1. At A particle is decelerating

2. At B particle is accelerating

3. At C particle has maximum velocity

4. At D particle has maximum acceleration