Question

A particle of mass $m$ is fixed to one end of a light spring of force constant $k$ and unstretched length $l$ . The system is rotated about the other end of the spring with an angular velocity $\omega $ , in gravity-free space. Then increase in the length of the spring will be:

• A. $\frac{m \, \omega ^{2} l}{k}$
• B. $\frac{m \, \omega ^{2} l}{k - m \, \omega ^{2}}$
• C. $\frac{m \, \omega ^{2} l}{k + m \, \omega ^{2}}$
• D. None of these

Answer 1

Answer: (B)

Let $x$ be increase in length of the spring. The particle would move in a circular path of radius $\left(\right.l+x\left.\right)$ . Centripetal force = force due to the spring
$m\left(l + x\right)\left(\omega \right)^{2}=kx$
$\therefore \, x=\frac{m \omega ^{2} l}{k - m \omega ^{2}}$