The potential energy of a long spring when stretched by $2\, cm$ is $U.$ If the spring is stretched by $8\, cm$ the potential energy stored in it is
$\frac{U}{4}$
$4U$
$8U$
$16U$
If the potential energy of a gas molecule is
$U = \frac{M}{{{r^6}}} - \frac{N}{{{r^{12}}}}$,
$M$ and $N$ being positive constants, then the potential energy at equilibrium must be
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 ?
A ball of mass $M$ falls from a height $h$ on a floor which the coefficient of restitution is $e$. The height attained by the ball after two rebounds is
A force of $\left( {2\widehat i + 3\widehat j + 4\widehat k} \right)\,N$ acts on a body for $4\, sec$ and produces a displacement of $\left( {3\widehat i + 4\widehat j + 5\widehat k} \right)\,m$. The power used is :- ............... $\mathrm{W}$
A curved surface is shown in figure. The portion $BCD$ is free of friction. There are three spherical balls of identical radii and masses. Balls are released from rest one by one from $A$ which is at a slightly greater height than $C$.
With the surface $AB$, ball $1$ has large enough friction to cause rolling down without slipping; ball $2$ has a small friction and ball $3$ has a negligible friction.
$(a)$ For which balls is total mechanical energy conserved ?
$(b)$ Which ball $(s)$ can reach $D$ ?
$(c)$ For ball which do not reach $D$, which of the balls can reach back $A$ ?