Physics Circle home Student Login

Home›Chapters›Work, Energy and Power PYQs›Potential Energy & Equilibrium›Question 9

JEE Main 2020 (6 Sep, Shift 1) · Potential Energy & Equilibrium

Potential Energy & Equilibrium question from JEE Main 2020 (6 Sep, Shift 1)

Q9JEE Main 2020 · 6 SEP · SHIFT 1Medium

Potential Energy & Equilibrium

If the potential energy between two molecules is given by

U = −Ar6+Br12-\frac{A}{r^6} + \frac{B}{r^{12}},

then at equilibrium, separation between molecules, and the potential energy are:

Show answer and solution

Answer: (a)

  1. dUdr=6Ar7−12Br13=0⇒r6=2BA\frac{dU}{dr} = \frac{6A}{r^7} - \frac{12B}{r^{13}} = 0 \Rightarrow r^6 = \frac{2B}{A}
  2. U=−Ar6+Br12=−A22B+BA24B2=−A24BU = -\frac{A}{r^6} + \frac{B}{r^{12}} = -\frac{A^2}{2B} + \frac{BA^2}{4B^2} = -\frac{A^2}{4B}
  3. So the answer is (a) (2BA)1/6,−A24B\left(\frac{2B}{A}\right)^{1/6}, -\frac{A^2}{4B}.
Report a mistake

More questions on Potential Energy & Equilibrium