Question

Earth is rotating about it's own axis and length of the day is 24hrs..Suddenly, if the earth shrinks.. Such that it's radius becomes half without changing its mass. Then, find the new length of the day.

Expecting Good answer!

Answer 1

hey there!


As $torque_{external} =0$

hence,

 $J_{initial} = J_{final}$             ( J=angular momentum)

$\frac{2}{5} M( \frac{r}{2} )^2 * \frac{2 \pi }{t'} = \frac{2}{5} Mr^2 * \frac{2 \pi }{t}$

by solving ,we get:                       ( $t' =$ new length of day)

[tex]t' = \frac{t}{4} [/tex]

         = $\frac{24}{4}$                     

$hence , t' = 6 hours$


#hope it helps!