Question

If the earth shrinks to half of its radius without changing its mass, the duration of the day will be

• A. $48hours$
• B. $24hours$
• C. $12hours$
• D. $6hours$

Answer 1

The correct option is D $6hours$

Angular momentum is conserved hence,

$L_i=L_f$

$I_I{\omega }_i=I_f{\omega }_f$

$\frac{2}{5}m{r}^2{\omega }_i=\frac{2}{5}m(\frac{r}{2}{)}^2{\omega }_f$

$\therefore {\omega }_f=4{\omega }_i$

or, $\frac{2\pi }{T_f}=4\times \frac{2\pi }{T_i}$

$\therefore T_f=\frac{T_i}{4}=\frac{24}{4}=6hours$