$A$ 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 $g = 10 \ m/s^2$)

$A$ sphere of mass $m$ travelling at constant speed $v$ strikes another sphere of the same mass. If the coefficient of restitution is $e$,then the ratio of the velocities of both spheres just after the collision is:

Consider a rubber ball freely falling from a height $h = 4.9\, m$ on a horizontal elastic plate. Assume that the duration of collision is negligible and the collision with the plate is totally elastic. Which one of the following graphs represents the velocity as a function of time and the height as a function of time?

$A$ $2 \, kg$ block is placed on a frictionless inclined plane with an angle of $30^\circ$ and a length of $2 \, m$. After reaching the bottom of the incline,it travels on a surface with a coefficient of friction of $0.25$. What distance (in $m$) will it travel on the surface before coming to rest?

$A$ man of mass $80 \ kg$ goes to the market on a scooter of mass $100 \ kg$ with a certain speed. On application of brakes,the stopping distance is $S_1$. The man returns home on the same scooter,with the same speed with a $60 \ kg$ bag of rice. If $S_2$ is the new stopping distance when the brakes are applied with the same force,then:

When a ball is freely fallen from a given height,it bounces to $80\%$ of its original height. What fraction of its mechanical energy is lost in each bounce?