Question

A boy stands over the centre of a horizontal platform which is rotating freely with a speed of $2$ revolutions/s about a vertical axis through the centre of the platform and straight up through the boy. He holds $2kg$ masses in each of his hands close to his body. The combined moment of inertia of the system is $1kg{m}^2$. The boy now stretches his arms so as to hold the masses far from his body. In this situation, the moment of inertia of the system increases to $2kg{m}^2$. The kinetic energy of the system in the latter case as compared with that in the previous case will

• A. Remain unchanged
• B. Decrease
• C. Increase
• D. Remain uncertain

Answer 1

The correct option is B Decrease

Angular momentum is conserved as: ${\tau }_{external}=0$

$I_i{w}_i=I_f{w}_f$

$\left(1kg{m}^2\right)w=\left(2kg{m}^2\right)w^{\prime }⟹w^{\prime }=\frac{w}{2}$

$K.E=\frac{1}{2}I{w}^2$

$\frac{E_1}{E_2}=\frac{I_1{w}_1^2}{I_2{w}_2^2}=\frac{\left(1kg{m}^2\right)w^2}{\left(2kg{m}^2\right)\frac{w^2}{4}}$

$\frac{E_2}{E_1}=\frac{1}{2}$

Thus K.E will decrease.