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

  • A

    Zero

  • B

    $M^2/4N$

  • C

    $NM^2/4$

  • D

    $MN^2/4$

Similar Questions

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

A stone tied to a string $L$ is whirled in a vertical circle, with the other end of the string at the centre. At a certain instant of time, the stone is as its lowest position and has a speed $u$. the magnitude of the change in its velocity as it reaches a position where the string is horizontal is

A basket and its contents have mass $M$. A monkey of mass $2M$ grabs the other end of the rope and very quickly (almost instantaneously) accelerates by pulling hard on the rope until he is moving with a constant speed of $v_{m/r} = 2ft/s$ measured relative to the rope. The monkey then continues climbing at this constant rate relative to the rope for $3$ seconds. How fast is the basket rising at the end of the $3$ seconds? Neglect the mass of the pulley and the rope. (given : $g = 32ft/s^2$)

A bomb of mass $9\, kg$ explodes into two pieces of masses $3\, kg$ and $6\, kg$. The velocity of mass $3\, kg$ is $16\, m/s$. The $KE$ of mass $6\, kg$ (in joule) is

System shown in figure is released from rest. Pulley and spring are massless and the friction is absent everywhere. The speed of $5\, kg$ block, when $2\, kg$ block leaves the contact with ground is (take force constant of the sprign $k = 40\, N/m$ and $g = 10\, m/s^2$)