Various types of potential energy are
(i) The energy possessed by the body due to gravitational force gives rise to gravitational potential energy.
The gravitational potential energy (U) at some height h is equal to the amount of work required to take the object from the ground to that height h.
U = mgh
(ii) The energy due to spring force and other similar forces give rise to elastic potential energy.
a) At the equilibrium position x = 0 potential energy is \(U=\frac{1}{2} k x^{2}\)
b) If the initial position is not zero and if the mass is changed from position x_i to x_f, if then elastic potential energy is \(U=\frac{1}{2} k\left(x_{f}^{2}-x_{i}^{2}\right)\)
(iii) The energy due to electrostatic force on charges gives rise to electrostatic potential energy.
Electrostatic potential energy is the work done to arrange two charges q₁ and q₂ at a separation \(r=\frac{1}{4 \pi \varepsilon_{0}} \frac{q_{1} q_{2}}{r^{2}}\)

Total energy is always conserved.
But K.E. is not conserved

\(\text {Mass of a bullet } m=20 g=20 \times 10^{-3} \mathrm{~kg} =0.02 \mathrm{~kg}  \)
\(\text {Mass of a pendulum } M =5 \mathrm{~kg}  \)
\(\text {Height } \mathrm{h} =10 \mathrm{~cm}  \)
\(=10 \times 10^{-2}  \)
\(=0.1 \mathrm{~m}  \)

\(\text { K.E. of the block } =\text { P.E. of the block }  \)
\(\frac{1}{2} M v^{2} =M g h  \)
\(\therefore v^{2} =\sqrt{2 g h}  \)
\(=\sqrt{2 \times 9.8 \times 0.1}=\sqrt{1.96}=1.4 \mathrm{~m} / \mathrm{s}  \)
\(\therefore \text { Final speed } v =1.4 \mathrm{~m} / \mathrm{s}  \)
\(\text {Final speed } v =\frac{m_{1} u_{1}+m_{2} u_{2}}{\left(m_{1}+m_{2}\right)}  \)
\(v_{1} =\frac{0.02 u_{1}+5 \times 0}{(0.02+5)}=\frac{0.02}{5.02} u_{1}  \)
\(\text { But } v =1.4  \)
\(\therefore 1.4 =\frac{0.02}{5.02} u_{1}  \)
\(u_{1}=\frac{1.4 \times 5.02}{0.02}=\frac{7.028}{0.02}=351.4 \mathrm{~m} / \mathrm{s}\)
\(\therefore \text { Initial speed } =351.4 \mathrm{~m} / \mathrm{s}\)

Given:
Force mg = 30 N; height = 10 m
Work done to lift a load W = ?
W = F.S (or) mgh
= 30 \(\times\) 10
W = 300J

Characteristics of elastic collision are
1. Total momentum remains conserved
2. Total kinetic energy remains conserved.
3. In elastic collision conservative forces are involved. Hence total kinetic energy is conserved.
4. In elastic collision, mechanical energy is not dissipated.
Characteristics of inelastic collision are
1. Total momentum is conserved.
2. Total kinetic energy is not conserved.
3. Forces involved are non-conservative forces
4. Mechanical energy is dissipated into heat, light, sound etc.