Question

A particle of mass $m$ is moving along the $x-axis$ under the potential $V(x)=\frac{k{x}^2}{2}+\frac{\lambda }{x^{{}^{\prime }}}$ where $k$ and $x^{{}^{\prime }}$ are positive constants of appropriate dimensions. The particle is slightly displaced from its equilibrium position. The particle oscillates with the angular frequency $\left(\omega \right)$ given by

• A. $3\frac{k}{m}$
• B. $3\frac{m}{k}$
• C. $\sqrt{\frac{k}{m}}$
• D. $\sqrt{3\frac{m}{k}}$
• E. $2\frac{m}{k}$

Answer 1

Answer: (C)

Given, $V(x)=\frac{k{x}^2}{2}+\frac{\lambda }{x^{{}^{\prime }}}$
$F=\frac{-\partial V(x)}{\partial x}=-kx$
$a=\frac{-k}{m}x$
${\omega }^2=\frac{k}{m}$
$\omega =\sqrt{\frac{k}{m}}$