Question

A particle of mass $m$ is fixed to one end of a light spring having force constant $k$ and unstretched length $l$. The other end is fixed. The system is given an angular speed $\omega$ about the fixed end of the spring such that it rotates in a circle in gravity free space. Then the stretch in the spring is :

• A. $\frac{ml\omega^{2}}{k - \omega m}$
• B. $\frac{ml\omega^{2}}{k - m\omega^{2}}$
• C. $\frac{ml\omega^{2}}{k + m\omega^{2}}$
• D. $\frac{ml\omega^{2}}{k + m\omega}$

Answer 1

Answer: (B)

$\frac{ml\omega^{2}}{k - m\omega^{2}}$

Answer 2

$kx=m\ell\omega^{2}+mx\omega^{2}$
$x-\frac{m\ell \omega ^{2}}{k-m\omega^{2}}$