Question 195 of 280
A solid sphere with uniform density and radius R is rotating initially with constant angular velocity about its diameter. After some time during the rotation its starts loosing mass at a uniform rate, with no change in its shape. The angular velocity of the sphere when its radius become is . The value of is ________
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Answer: 32
When sphere is of radius , its mass is , when radius is reduced to , mass will reduced to Now by conservation of angular momentum
$\begin{aligned}
& \left(\tau_{e x t}=0\right) \\
& L_1=L_2 \\
& I_1 \omega_1=I_2 \omega_2 \\
& \left(\frac{2}{5} M R^2\right) \omega_1=\left(\frac{2}{5}\left(\frac{\mathrm{M}}{8}\right)\left(\frac{\mathrm{R}}{2}\right)^2\right) \omega_2
\end{aligned}$
value of x is 32
Answer is 32
$\begin{aligned}
& \left(\tau_{e x t}=0\right) \\
& L_1=L_2 \\
& I_1 \omega_1=I_2 \omega_2 \\
& \left(\frac{2}{5} M R^2\right) \omega_1=\left(\frac{2}{5}\left(\frac{\mathrm{M}}{8}\right)\left(\frac{\mathrm{R}}{2}\right)^2\right) \omega_2
\end{aligned}$
value of x is 32
Answer is 32