Question

A rigid spherical body is spinning around an axis without any external torque. Due to change in temperature, the volume increases by $\text{1 \%}$. Its angular speed will

• A. Increase approximately by $\text{1 \%}$
• B. Decrease approximately by $\text{1 \%}$
• C. Decrease approximately by $\text{0.67 \%}$
• D. Decrease approximately by $\text{0.33 \%}$

Answer 1

Answer: (C)

Decrease approximately by $\text{0.67 \%}$

$\frac{4}{3}\pi R^3=V$

$⟹3\frac{\Delta R}{R}\times 100=\frac{\Delta V}{V}\times 100$

$3\frac{\Delta R}{R}\times 100=1$% i.e $R$ will increase by $0.33$%

As $I=Km{R}^2$

$⟹2\frac{\Delta R}{R}\times 100=\frac{\Delta I}{I}\times 100$

$\frac{\Delta I}{I}\times 100=0.67$% i.e $I$ increases by $0.67$%

As there is no external torque, thus $L=Iw=constant$

Hence, $w$ must decrease by $0.67$%.