Question

The acceleration due to gravity at the surface of the moon is 1.67 $\frac{m}{{sec}^2}$. If the radius of the moon is 1.74 $\times$ ${10}^6$ m. Find the mass of the moon. ( Given: G = 6.67 $\times$ ${10}^{-11}$ $\frac{N{m}^2}{{kg}^2}$)

Answer 1

Given,

$g_{moon}$ = 1.67 $\frac{m}{{sec}^2}$

$R_{moon}$ = 1.74 $\times$ ${10}^6$ m

We know that,

$g=\frac{GM}{R^2}$

So, $M=\frac{g{R}^2}{G}$ = $\frac{1.67\times ({1.74\times {10}^6)}^2}{6.67\times {10}^{-11}}$ = $7.58\times {10}^{22}kg$.

Thus, the mass of the moon is $7.58\times {10}^{22}kg$.