Question

If the earth were to suddenly contract to half the present radius (without any external torque acting on it), by how much would the day be decreased? (Assume earth to be a perfect solid sphere of moment of inertia $ \frac{2}{5}M{{R}^{2}} $ )

• A. $ 8\,h $
• B. $ 6\,h $
• C. $ 4\,h $
• D. $ 2\,h $
• E. $ 1\,h $

Answer 1

Answer: (B)

$ L={{I}_{1}}{{\omega }_{1}}={{I}_{2}}{{\omega }_{2}} $ $ \Rightarrow $ $ \frac{2}{5}M{{R}^{2}}\times \frac{2\pi }{{{T}_{1}}}=\frac{2}{5}M{{\left( \frac{R}{2} \right)}^{2}}\times \frac{2\pi }{{{T}_{2}}} $ $ \Rightarrow $ $ {{T}_{2}}=\frac{{{T}_{1}}}{4}=\frac{24}{4}=6\,h $