Question

Two men of equal masses stand at opposite ends of the diameter of a turntable disc of a certain mass, moving with constant angular velocity. The two men make their way to the middle of the turntable at equal rates. In doing so will

• A. kinetic energy of rotation has increased while angular momentum remains same.
• B. kinetic energy of rotation has decreased while angular momentum remains same.
• C. kinetic energy of rotation has decreased but angular momentum has increased.
• D. both, kinetic energy of rotation and angular momentum have decreased.

Answer 1

Answer: (B)

kinetic energy of rotation has decreased while angular momentum remains same.

Potential energy $U=mV$
$\Rightarrow U=(50x^2+100){10}^{-2}$
$F=-\frac{dU}{dx}=-\left(100x\right){10}^{-2}$
$\Rightarrow m{\omega }^{2}x=-(100\times {10}^{-2})x$
$10\times {10}^{-3}{\omega }^{2}x=100\times {10}^{-2}x\Rightarrow {\omega }^2=100,\omega =10$
$\Rightarrow f=\frac{\omega }{2\pi }=\frac{10}{2\pi }=\frac{5}{\pi }$