Question

If the mass of the earth is doubled and the distance of the moon revolving around the earth is also doubled, then, find the new time period of revolution of moon. (Take the present time of revolution as $28$ days)

• A. 6
• B. 36
• C. 56
• D. 112

Answer 1

The correct option is C 56

As we know

$T^2=\frac{4{\pi }^2}{GM}{r}^3.....1T^{\prime 2}=\frac{4{\pi }^2}{G.2M}(2r{)}^3........2$

Taking Ratio,

$\therefore \frac{{T^2}^{\prime }}{T^2}=\frac{\frac{4{\pi }^2}{GM}.\frac{{8r}^3}{2}}{\frac{4{\pi }^2}{GM}{r}^3}$

$=>{T^2}^{\prime }=4T^2=2\times 28=56$