Question

If the earth shrinks such that its mass does not change but radius decreases to one quarter of its original value then one complete day will take:

• A. 96 h
• B. 48 h
• C. 6 h
• D. 1.5 h

Answer 1

The correct option is D 1.5 h

We know that angular momentum of spin $=I\omega$
Bythe conservation of angular momentum
$\frac{2}{5}M{R}^2.\frac{2\pi }{T}=\frac{2}{5}M{\left(\frac{R}{4}\right)}^2.\frac{2\pi }{T^{\prime }}$
$T^{\prime }=\frac{T}{16}=\frac{24}{16}=1.5h$