Two persons $A$ and $B$ are throwing a ball of mass $200 \ g$ at a wall as shown in the figure. The balls strike the wall perpendicularly at the same point at a height of $2 \ m$ from the ground. The balls strike the wall elastically at the same time and return back to $A$ and $B$ at the same time. They repeat this process. What is the average force exerted on the wall (in $N$)? (Take $g = 10 \ m/s^2$)

$A$ bead of mass $m$ slides without friction on the wall of a vertical circular hoop of radius $R$ as shown in the figure. The bead moves under the combined action of gravity and a massless spring of constant $k$ attached to the bottom of the hoop. The natural (equilibrium) length of the spring is $R$. If the bead is released from the top of the hoop with negligible initial speed,what is the velocity of the bead when the length of the spring becomes $R$? ($g$ is the acceleration due to gravity)

$A$ body of mass $4 \,kg$ is moving with momentum of $8 \,kg \,m/s$. $A$ force of $0.2 \,N$ acts on it in the direction of motion of the body for $10 \,s$. The increase in kinetic energy in joules is

Three blocks $A, B$ and $C$ are lying on a smooth horizontal surface,as shown in the figure. $A$ and $B$ have equal masses $m$,while $C$ has mass $M$. Block $A$ is given an initial speed $v$ towards $B$,due to which it collides with $B$ perfectly inelastically. The combined mass then collides with $C$,also perfectly inelastically. If $5/6^{th}$ of the initial kinetic energy is lost in the whole process,what is the value of $M/m$?

$A$ ball of mass $0.2 \ kg$ is thrown vertically upwards by applying a force by hand. If the hand moves $0.2 \ m$ while applying the force and the ball goes up to $2 \ m$ height further,find the magnitude of the force $F$ in $N$. (Consider $g = 10 \ m/s^2$)

Two cars,both of mass $m$,collide and stick together. Prior to the collision,one car had been traveling north at speed $2v$,while the second was traveling at speed $v$ at an angle $\phi$ south of east (as indicated in the figure). The magnitude of the velocity of the two-car system immediately after the collision is: