Question

If the radius of the earth contracts to half of its present value without change in its mass what will be the new duration of the day in hours

• A. 3h
• B. 4h
• C. 5h
• D. 6h

Answer 1

The correct option is

C

6h

Present angular momentum of earth $L_1=I\omega =\frac{2}{5}M{R}^2\omega$

New angular because of change in radius $L_2=\frac{2}{5}M{\left(\frac{R}{2}\right)}^2{\omega }^{\prime }$

If external torque is zero then angular momentum must be conserved $L_1=L_2$

$\frac{2}{5}M{R}^2\omega =\frac{1}{4}\times \frac{2}{5}M{R}^2{\omega }^{\prime }$ i.e., ${\omega }^{\prime }=4\omega ;T^{\prime }=\frac{1}{4}T=\frac{1}{4}\times 24=6h$

Hence, new duration of the day will be 6 hours