Question

Density remaining constant, if earth contracts to half of its present radius, duration of the day would be (in minutes):

• A. $360$
• B. $80$
• C. $100$
• D. $120$

Answer 1

The correct option is A $360$

Now if density remains same, new moment of inertia will be $I^{\prime }=\frac{I}{4}$

And according to law of conservation of angular momentum $\left(I\omega \right)=\left(I^{\prime }{\omega }^{\prime }\right)$

${\omega }^{\prime }=4\omega$

Also, $\omega =\frac{2\pi }{T}$ and ${\omega }^{\prime }=\frac{2\pi }{T^{\prime }}$

$T^{\prime }=\frac{T}{4}$

$T=24hrs$

$T^{\prime }=\frac{24}{4}$

$T^{\prime }=6hrs=360minutes$

Hence a day would be one-fourth of current duration