$A$ smooth sphere of mass $m$ moving with velocity $u$ collides with another smooth sphere of mass $2m$ at rest. What is the range of the velocity $v$ of the second sphere after the collision?

$A$ 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 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

$A$ small block of mass $200 \ g$ is placed on a horizontal slab at a height of $2 \ m$ above the floor. The block is pressed against a horizontal spring fixed at one end to compress the spring by $10.0 \ cm$. Upon releasing, the block moves horizontally until it leaves the spring. Calculate the horizontal distance covered by the block after leaving the slab and just before hitting the ground. The spring constant is $50 \ N \ m^{-1}$. (Assume $g = 10 \ m \ s^{-2}$) (in $m$)

$A$ ball falls freely from rest on to a hard horizontal floor and repeatedly bounces. If the velocity of the ball just before the first bounce is $7 \text{ m/s}$ and the coefficient of restitution is $0.75$. The total distance travelled by the ball before it comes to rest is (acceleration due to gravity $= 10 \text{ m/s}^2$) (in $\text{ m}$)

Two bodies $A$ and $B$ of masses $20 \ kg$ and $5 \ kg$ respectively are at rest. Due to the action of a force of $40 \ N$ separately,if the two bodies acquire equal kinetic energies in times $t_A$ and $t_B$ respectively,then $t_A: t_B=$