First slide

Law of conservation of angular momentum

Question

If the mass of earth and radius suddenly becomes 2 times and 1/4 th of the present value respectively, the length of the day becomes

Moderate

A

24 hr
B

6 hr
C

3/2 hr
D

3 hr

Solution

$\large {T_1} = 24hr;\;{I_1}{w_1} = {I_2}{w_2}$
$\large \frac{2}{5}{M_1}R_1^2.\frac{{2\pi }}{{{T_1}}} = \frac{2}{5}{M_2}R_2^2.\frac{{2\pi }}{{{T_2}}}$
$\large \frac {M_1R_1^2}{T_1}=\frac {(2M_1)(R_1/4)^2}{T_2}\Rightarrow \frac {M_1R_1^2}{T_1}=\frac 2{16}\frac {M_1R_1^2}{T_2}$
$\large {T_2} = \frac{{{T_1}}}{8} = \frac{{24}}{8} = 3hr$

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