A particle of mass m is executing oscillations about the origin on the x-axis with amplitude A. Its potential energy is given as $U (x) = α x^{4}$ where $α$ is a positive constant. The x-coordinate of the particle where its potential energy is one third the corresponding kinetic energy is

see full answer

Take the SCORE scholarship exam from home and compete for scholarships worth ₹1 crore!*

An Intiative by Sri Chaitanya

\pm \frac{A}{\sqrt{3}}

\pm \frac{A}{2}

\pm \frac{A}{\sqrt{2}}

\pm \frac{A}{3}

answer is B.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

Potential energy

= a x^{4}

Potential energy, $u = \frac{1}{3}$ kinetic energy

$k = 3 u$

$k = 3 a x^{4}$

At maximum amplitude A

Total energy, $E = {aA}^{4}$

$E = u + k$

${aA}^{4} = a x^{4} + 3 a x^{4}$

$x^{4} = \frac{A^{4}}{4}$

$x^{2} = \pm \frac{A^{2}}{2}$

$x = \pm \sqrt{\frac{A^{2}}{2}}$

$x = \pm \frac{A}{\sqrt{2}}$

Watch 3-min video & get full concept clarity