$A$ ball of mass $m$ moves with speed $v$ and strikes a wall having infinite mass and it returns with the same speed. Then the work done by the ball on the wall is:

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?

Two massless strings of length $5\, m$ hang from the ceiling very near to each other as shown in the figure. Two balls $A$ and $B$ of masses $0.25\, kg$ and $0.5\, kg$ are attached to the strings. The ball $A$ is released from rest at a height of $0.45\, m$ as shown in the figure. The collision between the two balls is completely elastic. Immediately after the collision,the kinetic energy of ball $B$ is $1\, J$. The velocity of ball $A$ just after the collision is

State whether the following statements are true or false:
$(a)$ If the magnitude of force and length are increased by $4$ times,the magnitude of energy increases by $16$ times.
$(b)$ In an inelastic collision,both momentum and energy are conserved.
$(c)$ If work is done on a system by non-conservative forces,the potential energy increases.

$A$ force exerts an impulse $I$ on a particle changing its speed from $u$ to $2u$. The applied force and the initial velocity are oppositely directed along the same line. The work done by the force is

$A$ force of $10 \ N$ acting at an angle on a particle produces a displacement of $(3 \hat{i} - 4 \hat{\jmath}) \ m$. Due to this force,if the kinetic energy of the particle is decreased by $25 \ J$,then the angle between the force and the displacement is: