Question

A circular platform is mounted on a frictionless vertical axle. Its radius R=2m and its moment of inertia about the axle is $200kg{m}^2$. It is initially at rest. A 50 kg man stands on the edge of the platform and begins to walk along the edge at the speed of $1m{s}^{-1}$ relative to the ground. Time taken by the man to compete one revolution with respect to disc is:

• A. $\pi s$
• B. $\frac{3\pi }{2}s$
• C. $2\pi s$
• D. $\frac{\pi }{2}s$

Answer 1

The correct option is C $2\pi s$

$I=200kg{m}^2$

Since no external force is acting on the system containing discs and man so angular momentum must be conserved.

$mvr=I\omega$

$50\times 2=200\omega$

$\omega =\frac{1}{2}rad{s}_{-1}$

$v=r\omega$

$v=1m/s$ in opposite direction .So effective velocity of man relative to ground is 2 m/s

Time taken $=\frac{2\pi \times 2}{2}=2\pi sec$