Question

A block of mass m is tied to a spring of spring constant k, natural length l, and the other end of spring is fixed at O. If the block moves in a circular path on a smooth horizontal surface with constant angular velocity $\omega$, find the tension in the spring.

Answer 1

Assume extension in the spring is x
Here centripetal force is provided by spring force.
Centripetal force, $kx=m{\omega }^2(l+x)$
$\Rightarrow x=\frac{m{\omega }^{2}l}{k-m{\omega }^2}$
therefore,
Tension = $kx=\frac{km{\omega }^{2}l}{k-m{\omega }^2}$