Question

A disc of mass M and radius R is free to rotate about its vertical axis as shown in the figure. A battery operated motor of negligible mass is fixed to this disc at a point on its circumference. Another disc of the same mass M and radius \(R / 2\) is fixed to the motor's thin shaft. Initially, both the discs are at rest. The motor is switched on so that the smaller disc rotates at a uniform angular speed \(\omega\). If the angular speed at which the large disc rotates is \(\omega / n\), then the value of n is ____.

Answer 1

Correct answer is : 12

On applying conservation of angular momentum about axis of larger disc.

\(\frac {1}{2}.M \left(\frac {R}{2}\right)^2 . \omega - M (\omega 'R).R - \frac {MR^2}{2}. \omega '=0\)

\(\Rightarrow \frac {\omega}{8} = \frac {3\omega '}{2}\)

\(\Rightarrow \omega' = \frac {\omega}{12}\)

Hence, n = 12