Question

A merry-go-round, made of a ring-like platform of radius $R$ and mass $M$, is revolving with angular speed $\omega$. $A$ person of mass $M$ is standing on it. At one instant, the person jumps off the round, radially away from the centre of the round. The speed of the round afterwards is

• A. $2\omega$
• B. $\omega$
• C. $\frac{\omega}{2}$
• D. $0$

Answer 1

Answer: (A)

Here angular momentum is converted
$L _{ i }= L _{ f }$
$\left( I _{\text {ring }}+ M R ^{2}\right) \omega=\left( L _{\text {man }}+ L _{\text {ring }}\right) \omega' \,\,\,L _{\text{man}}= L _{\text {ring }}$
[A man is assumed to at circumstances of ring and is final angular speed of ring after men jump off]
$\left( M R ^{2}+ M R ^{2}\right) \omega= O + M R ^{2} \omega '$
$2 \omega=\omega'$