A mouse of mass $\mathrm{m}$ jumps on the outside edge of a rotating ceiling fan of moment of inertia I and radius $\mathrm{R}$. The fractional loss of angular velocity of the fan as a result is

Question

A mouse of mass $\mathrm{m}$ jumps on the outside edge of a rotating ceiling fan of moment of inertia I and radius $\mathrm{R}$. The fractional loss of angular velocity of the fan as a result is, $\frac{m R^2}{\mathrm{I}+\mathrm{mR}^2}$, $\frac{I}{I+m R^2}$, $\frac{\mathrm{I}-\mathrm{mR}^2}{\mathrm{I}}$, $\frac{I-m R^2}{I+m R^2}$

MARKS App · Accepted Answer

Hint : $I \omega_0=\left(\mathrm{I}+\mathrm{mR}^2\right) \omega$ $\omega_0 \rightarrow$ Initial angular velocity $\omega=\frac{I \omega_0}{I+m R^2}$ $\omega \rightarrow$ Final angular velocity So, $\frac{\omega_0-\omega}{\omega_0}=I-\frac{I}{I+m R^2}=\frac{m R^2}{I+m R^2}$

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