Question

A uniform disc of mass $100 \,kg$ and radius $2\, m$ is rotating at $1 rad / s$ about a perpendicular axis passing through its centre. A boy of mass $60\, kg$ standing at the centre of the disk suddenly jumps to a point which is $1\, m$ 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, $I_{1} \omega_{1}=I_{2} 2 \omega_{2}$
$\Rightarrow \,\left(\frac{1}{2} M_{ disc } \times R_{ disc }^{2}\right) \omega_{1}=\left(\frac{1}{2} M_{ disc } R_{ disc }^{2}+M_{ boy } R_{ boy }^{2}\right) \omega_{2}$
$\Rightarrow \,\left(\frac{1}{2} \times 100 \times 2^{2}\right) \times 1=\left(\frac{1}{2} \times 100 \times 2^{2}+60 \times 1^{2}\right) \times \omega_{2}$
$\Rightarrow \, \omega_{2}=\frac{200}{200+60}$
$=0.77 \,rad - s ^{-1}$