Question

A man of $80kg$ mass is standing on the rim of a circular platform of mass $200kg$ rotating about its axis. The mass of the platform with the man on it rotates at $12.0rpm$. If the man now moves to centre of the platform, the rotational speed would become

• A. 16.5 rpm
• B. 25.7 rpm
• C. 32.3 rpm
• D. 31.2 rpm

Answer 1

Answer: (D)

Here, mass of man, $m=80kg$
Mass of platform, $M=200kg$
Let $R$ be the radius of platform.
When man is standing on the rim,
$I_1=M(R/2{)}^2+m{R}^2$
$={\left(\frac{R}{2}\right)}^2(M+4m)$
When man reaches the centre of platform,
$I_2=M(R/2{)}^2+m\times 0=m(R/2{)}^2$
As angular momentum is conserved,
$\frac{I_1}{I_2}-\frac{{\omega }_2}{{\omega }_1}-\frac{2\pi n_2}{2\pi n_1}-\frac{n_2}{n_1}$
$n_2=\frac{I_1}{I_2}\times n_2$
$=\frac{(M+4m)(R/2{)}^2}{M(R/2{)}^2}\times 12$
$=\frac{(200+4\times 80)}{200}\times 12$
$=\frac{520\times 12}{200}$
$n_1=31.2$ rpm