Two bodies $A$ and $B$ of masses $5.00 \ kg$ and $10.0 \ kg$ respectively,moving in opposite directions with velocities $4.00 \ m/s$ and $0.50 \ m/s$ respectively,make a head-on collision in free space. The force of their mutual interaction varies according to the given graph. The coefficient of restitution is

$A$ particle of mass $M$ moving along the $X$-axis with speed $V_0$ collides with and sticks to another particle of mass $m$ moving along the $Y$-axis with speed $V_0$. What will be the velocity of the combined mass after the collision?

$A$ tennis ball dropped from a height of $2 \,m$ rebounds only $1.5 \,m$ after hitting the ground. What fraction of its energy is lost in the impact?

$A$ 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 $10 \; m s^{-1}$?

$A$ block of mass $0.18 \ kg$ is attached to a spring of force constant $2 \ N/m$. The coefficient of friction between the block and the floor is $0.1$. Initially,the block is at rest and the spring is unstretched. The block is pushed as shown in the figure. The block slides a distance of $0.06 \ m$ and comes to rest. If the initial velocity of the block is $V = N/10 \ m/s$,then what is the value of $N$?

The quantities remaining constant in a general collision are