A ball $P$ collides with another identical ball $Q$ at rest. For what value of coefficient of restitution $e$, the velocity of ball $Q$ become two times that of ball $P$ after collision
$\frac{1}{3}$
$\frac{1}{2}$
$\frac{1}{4}$
$\frac{1}{6}$
Work equal to $25\,J$ is done on a mass of $2\,kg$ to set it in motion. If whole of it is used to increase the kinetic energy then velocity acquired by the mass is ............ $\mathrm{m}/ \mathrm{s}$
A cord is used to lower vertically a block of mass $M$ by a distance $d$ with constant downward acceleration $\frac{g}{4}$. Work done by the cord on the block is
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 $A$ ?
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
Work done by the frictional force is