$A$ man throws a ball with a speed of $12 \ m/s$ at a height of $12 \ m$. If he throws the ball such that it just reaches this height,what is the percentage of energy saved?

$A$ small disc of mass $m$ slides down with initial velocity zero from the top $(A)$ of a smooth hill of height $H$ having a horizontal portion $(BC)$ as shown in the figure. If the height of the horizontal portion of the hill is $h$,then the maximum horizontal distance covered by the disc from the point $D$ is

Explain why total linear momentum is conserved in an elastic collision,and define inelastic collision and perfectly inelastic collision.

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.

$A$ toy of mass $20 \,g$ at rest acquires a velocity $(3 \hat{i}-2 \hat{j}) \,m/s$ in $2 \,s$. The power of the toy is: (in $\,W$)

Two solid rubber balls $A$ and $B$ have masses $200 \ g$ and $400 \ g$ respectively. They are moving towards each other,with ball $A$ having a velocity of $0.3 \ m/s$. After the collision,both balls come to rest. What is the velocity of ball $B$ in $m/s$?