In a gamma decay process, the internal energy of a nucleus of mass $M$ decreases, a gamma photon of energy $E$, a linear momentum $\frac{E}{c}$ is emitted and the nucleus recoils. Find the decrease in internal energy.

A block of mass $2.0 \mathrm{kg}$ is moving on a frictionless horizontal surface with a velocity of $1.0 \mathrm{m} {\mathrm{s}}^{-1}$ towards another block of equal mass kept at rest. The spring constant of the spring fixed at one end is $100 \mathrm{N} {\mathrm{m}}^{-1}$. Find the maximum compression of the spring.

A bullet of mass $20 \mathrm{g}$ travelling horizontally with a speed of $500 \mathrm{m} {\mathrm{s}}^{-1}$ passes through a wooden block of mass $10.0 \mathrm{kg}$, initially at rest on a levelled surface. The bullet emerges with a speed of $100 \mathrm{m} {\mathrm{s}}^{-1}$ and the block slides $20 \mathrm{cm}$ on the surface before coming to rest. Find the friction coefficient between the block and the surface.

A ball falls on an inclined plane of inclination $\mathrm{\theta }$ from a height $h$ above the point of impact and makes a perfectly elastic collision. Where does the ball hit the plane again? Solve the previous problem if the coefficient of restitution is $e$.

Use $\mathrm{\theta }=45°$, $e=\frac{3}{4}$ and $h=5 \mathrm{m}$.

A block of mass $200 \mathrm{g}$ is suspended through a vertical spring. The spring is stretched by $1.0 \mathrm{cm}$ when the block is in equilibrium. A particle of mass $120 \mathrm{g}$ is dropped on the block from the height of $45 \mathrm{cm}$. The particle sticks to the block after the impact. Find the maximum extension of the spring. Take $g=10 \mathrm{m} {\mathrm{s}}^{-2}$.

A bullet of mass $25 \mathrm{g}$ is fired horizontally into a ballistic pendulum of mass $5.0 \mathrm{kg}$ and gets embedded in it (figure). If the centre of the pendulum rises by a distance of $10 \mathrm{cm},$ find the speed of the bullet.