Question

A uniform disc of mass $100kg$ and radius $2m$ is rotating at $1rad/s$ about a perpendicular axis passing through its centre. A boy of mass $60kg$ standing at the centre of the disk suddenly jumps to a point which is $1m$ from the centre of the disc. The final angular velocity of the boy (in $rad/s)$ is

• A. 0.77
• B. 0.5
• C. 41
• D. 2

Answer 1

Answer: (A)

Angular momentum is conserved as there is no external torque.
So, $I_1{\omega }_1=I_{2}2{\omega }_2$
$\Rightarrow \left(\frac{1}{2}{M}_{disc}\times R_{disc}^2\right){\omega }_1=\left(\frac{1}{2}{M}_{disc}{R}_{disc}^2+M_{boy}{R}_{boy}^2\right){\omega }_2$
$\Rightarrow \left(\frac{1}{2}\times 100\times 2^2\right)\times 1=\left(\frac{1}{2}\times 100\times 2^2+60\times 1^2\right)\times {\omega }_2$
$\Rightarrow {\omega }_2=\frac{200}{200+60}$
$=0.77rad-s^{-1}$