Question

If the mass of earth were $4$ times the present mass, the mass of the moon were half the present mass and the moon were revolving round the earth at the same present distance, the time period of revolution of the moon would be approximately.

• A. $56$ days
• B. $28$ days
• C. $14$ days
• D. $7$ days

Answer 1

The correct option is C $14$ days

Time period of moon is given by:
$T^2=\frac{4{\pi }^2}{GM}{r}^3$, where $M$ is the mass of the Earth.

$T=27$days

When mass of the Earth is $4M$,
${T^{{}^{\prime }}}^2=\frac{4{\pi }^2}{4MG}{r}^3=\frac{T^2}{4}$
$\Rightarrow T^{{}^{\prime }}=\frac{T}{2}=\frac{27}{2}=14$ days