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
$L_i=L_f$
$\left(I_{\text{ring }}+M{R}^2\right)\omega =\left(L_{\text{man }}+L_{\text{ring }}\right){\omega }^{\prime }{L}_{\text{man}}=L_{\text{ring }}$
[A man is assumed to at circumstances of ring and is final angular speed of ring after men jump off]
$\left(M{R}^2+M{R}^2\right)\omega =O+M{R}^2{\omega }^{\prime }$
$2\omega ={\omega }^{\prime }$