If the potential energy of a gas molecule is& | vedclass

Name: PDF Generator App | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

$\mathrm{F}=\frac{\mathrm{d} \mathrm{U}}{\mathrm{dr}}=-\frac{\mathrm{d}}{\mathrm{dr}}\left[\frac{\mathrm{M}}{\mathrm{r}^{6}}-\frac{\mathrm{N}}{\mathrm

Vedclass · Accepted Answer

$\frac {M^2}{4N}$

Vedclass · Answer

$\mathrm{F}=\frac{\mathrm{d} \mathrm{U}}{\mathrm{dr}}=-\frac{\mathrm{d}}{\mathrm{dr}}\left[\frac{\mathrm{M}}{\mathrm{r}^{6}}-\frac{\mathrm{N}}{\mathrm{r}^{12}}ight]$

$=-\left[-\frac{6 \mathrm{M}}{\mathrm{r}^{7}}+\frac{12 \mathrm{N}}{\mathrm{r}^{13}}ight]$

In equilibrium position, $F=0$

$	herefore \quad \frac{6 \mathrm{M}}{\mathrm{r}^{7}}-\frac{12 \mathrm{N}}{\mathrm{r}^{13}}=0$

Or         $r^{6}=\frac{2 N}{M}$

Potential energy at equilibrium position,

$\mathrm{U}=\frac{\mathrm{M}}{(2 \mathrm{N} / \mathrm{M})}-\frac{\mathrm{N}}{(2 \mathrm{N} / \mathrm{M})^{2}}$

$=\frac{M^{2}}{2 N}-\frac{M^{2}}{4 N}=\frac{M^{2}}{4 N}$

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

Similar Questions

A particle of mass $4\, m$ which is at rest explodes into three fragments. Two of the fragments each of mass $m$ are found to move with a speed $v$ each in perpendicular directions. The total energy released in the process will be

In the figure shown the potential energy $(U)$ of a particle is plotted against its position $'x'$ from origin. The particle at

$A$ ball is dropped from height $5m$. The time after which ball stops rebounding if coefficient of restitution between ball and ground $e = 1/2$, is .................. $\mathrm{sec}$

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 ball is dropped from height $h$ on a plane. If the coefficient of restitution of the plane is $e$ and if ball hits ground two times, the height upto which it reaches after two jumps, will be