$A$ bullet of mass $0.01\,kg$ and travelling at a speed of $500\,m/s$ strikes a block of mass $2\,kg$ which is suspended by a string of length $5\,m$. The centre of gravity of the block is found to rise a vertical distance of $0.1\,m$. What is the speed of the bullet after it emerges from the block?

$A$ block of mass $1 \ kg$ is moved by a distance of $1 \ m$ on a horizontal surface by applying a force of $8 \ N$. Then it is lifted to a height of $2 \ m$. The total work done is ... $J$. (Take $g = 10 \ m/s^2$)

The figure below shows a small mass connected to a string,which is attached to a vertical post. If the ball is released when the string is horizontal as shown below,the magnitude of the total acceleration (including radial and tangential) of the mass as a function of the angle $\theta$ is

An engine is attached to a wagon through a shock absorber of length $1.5\, \text{m}$. The system with a total mass of $40,000\, \text{kg}$ is moving with a speed of $72\, \text{km/h}$ when the brakes are applied to bring it to rest. In the process of the system being brought to rest,the spring of the shock absorber gets compressed by $1.0\, \text{m}$. If $90\, \%$ of the energy of the wagon is lost due to friction,the spring constant is $....\, \times 10^{5}\, \text{N/m}$.

In the diagram shown,there is no friction at any contact surface. Initially,the spring has no deformation. What will be the maximum deformation in the spring? Consider all the strings to be sufficiently large. Consider the spring constant to be $K$.

$A$ bolt of mass $0.3 \; kg$ falls from the ceiling of an elevator moving down with a uniform speed of $7 \; m s^{-1}$. It hits the floor of the elevator (length of the elevator $= 3 \; m$) and does not rebound. What is the heat produced by the impact? Would your answer be different if the elevator were stationary?