$A$ 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

$A$ man of mass $60$ $kg$ wants to lose $5$ $kg$ of mass by climbing up and down stairs. Assume that twice the amount of fat is burned while climbing up compared to climbing down. If burning $1$ $kg$ of fat provides $7000$ $kcal$ of energy, how many times must he climb up and down the stairs to lose $5$ $kg$ of mass (in $times$)? (Assume the energy spent in climbing up is $20$ $kcal$ and climbing down is $10$ $kcal$ per trip).

From a building, two balls $A$ and $B$ are thrown such that $A$ is thrown upwards and $B$ is thrown downwards (both vertically) with the same speed. If $v_A$ and $v_B$ are their respective velocities on reaching the ground, then:

$A$ bullet of mass $m$ moving with velocity $v_1$ strikes a wooden block of mass $M$ suspended as shown in the figure and gets embedded in it. If the block rises to a height $h$,what is the initial velocity of the bullet?

$A$ body of mass $5\,kg$ is moving with a momentum of $10\,kg\,m/s$. Now a force of $2\,N$ acts on the body in the direction of its motion for $5\,s$. The increase in the kinetic energy of the body is $...........J$.

$A$ rain drop of radius $2 \; mm$ falls from a height of $500 \; m$ above the ground. It falls with decreasing acceleration (due to viscous resistance of the air) until at half its original height,it attains its maximum (terminal) speed,and moves with uniform speed thereafter. What is the work done by the gravitational force on the drop in the first and second half of its journey? What is the work done by the resistive force in the entire journey if its speed on reaching the ground is $10 \; m s^{-1}$?