Question

A small meteorite of mass 'm' travelling towards the centre of earth strikes the earth at the equator. The earth is a uniform sphere of mass 'M' and radius 'R'. The length of the day was 'T' before the meteorite struck. After the meteorite strikes the earth, the length of day increases (in sec) by

• A. $\frac{5mT}{2M}$
• B. $\frac{m}{M}T$
• C. $\frac{4mT}{5M}$
• D. $\frac{M}{3mT}$

Answer 1

The correct option is A $\frac{5mT}{2M}$

$I_1{\omega }_1=I_2{\omega }_2$
$\frac{2}{5}M{R}^2\times \left(\frac{2\pi }{T_1}\right)=(\frac{2}{5}M{R}^2+m{R}^2)\frac{2\pi }{T_2}$
$\frac{T_2}{T_1}=1+\frac{5m}{2M}$
$\frac{T_2-T_1}{T_1}=\frac{5m}{2M}$
$T_2-T_1=\frac{5mT}{2M}$ $[i.e;T_1=T]$