Question

A circular turn table of radius 0.5 m has a smooth groove as shown in figure. A ball of mass 90 g is placed inside the groove along with a spring of spring constant ${10}^{2}N/cm$. The ball is at a distance of 0.1 m from the centre when the turn table is at rest. On rotating the turn table with a constant angular frequency of ${10}^2{sec}^{-1}$, the ball moves away from the centre by a distance nearly equal to

• A. ${10}^{-1}m$
• B. ${10}^{-2}m$
• C. ${10}^{-3}m$
• D. $2\times {10}^{-1}m$

Answer 1

Answer: (B)

${10}^{-2}m$

When the turn table rotates with angular speed $\varpi$, the particle of mass m describes a circle of radius r. The centrifugal force experienced is

$mr{\varpi }^2=(9\times {10}^{-2})\left({10}^{-1}\right)({10}^2{)}^2=9\times 10N$

As a result of this force the spring is compressed by a distance x. The restoring force of the spring = $kx={10}^{4}x$

In equilibrium, $9\times 10={10}^{4}x$

$\Rightarrow x\approx {10}^{-2}m$