$A$ wedge of mass $M = 4m$ lies on a frictionless plane. $A$ particle of mass $m$ approaches the wedge with speed $v$. There is no friction between the particle and the plane or between the particle and the wedge. The maximum height climbed by the particle on the wedge is given by

$A$ 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?

$A$ spring-block system is resting on a frictionless floor as shown in the figure. The spring constant is $2.0 \,N \,m^{-1}$ and the mass of the block is $2.0 \,kg$. Ignore the mass of the spring. Initially, the spring is in an unstretched condition. Another block of mass $1.0 \,kg$ moving with a speed of $2.0 \,m \,s^{-1}$ collides elastically with the first block. The collision is such that the $2.0 \,kg$ block does not hit the wall. The distance, in metres, between the two blocks when the spring returns to its unstretched position for the first time after the collision is. . . .

$A$ block of mass $5 \ kg$ is lifted to a height of $5 \ m$ by a force of $60 \ N$. Find:
$(1)$ Work done by the force.
$(2)$ Potential energy of the block at $5 \ m$.
$(3)$ Kinetic energy of the block at $5 \ m$.
$(4)$ Velocity of the block at $5 \ m$. (Take $g = 9.8 \ m/s^2$)

$A$ body of mass $m$ is dropped from a height of $h$. Simultaneously,another body of mass $2m$ is thrown vertically upward with such a velocity $v$ that they collide at a height $h/2$. If the collision is perfectly inelastic,the velocity at the time of collision with the ground will be:

Calculate the work done to pull a block of mass $M$ by a constant force $F$ as shown in the figure. The coefficient of friction between the block and the ground is $\mu$.