Question

A ring attached with a spring is fitted in a smooth rod. The spring is fixed at the outer end of the rod. The mass of the ring is $3kg$ and spring constant of the spring is $300N/m$. The ring is given a velocity $V$ towards the outer end of the rod. And the rod is set to be rotating with an angular velocity $\omega$. The ring will move with constant speed with respect to the rod if:

• A. angular velocity of rod is increased continuously
• B. $\omega =10rad/s$
• C. angular velocity of rod is decreased continuously
• D. constant velocity of ring is not possible

Answer 1

Answer: (B)

$\omega =10rad/s$

For the ring to move in a circle at constant speed the net force on it should be zero. Here spring force will provide the necessary centripetal force.

$\therefore kx=mx{\omega }^2$
$\Rightarrow \omega =\sqrt{\frac{k}{m}}=\sqrt{\frac{300}{3}}=10rad/s.$