Question

If the radius of earth shrinks by $0.2$% without change in its mass, the % change in its angular velocity is:

• A. increase by $0.4$%
• B. increase by $0.1$%
• C. decrease by $0.4$%
• D. decrease by $0.1$%

Answer 1

The correct option is A increase by $0.4$%

$R^{\prime }=\frac{998R}{1000}$

Since, $I\omega =\frac{2}{5}M{R}^2\omega$ and $\omega \propto R^{-2}$

$\frac{\Delta \omega }{\omega }=-2\frac{R^{\prime }-R}{R}=-2\left(\frac{-2R}{1000R}\right)$

$\frac{\Delta \omega }{\omega }=\frac{+4R}{1000R}=0.4\%$

+ve sign indicates that the final $\omega$ increases by $0.4\%$.