Question

The mass of earth is $80$ times that of moon and its diameter is double that of moon. If the value of acceleration due to gravity on earth is $9.8m/s^2$, then the value of acceleration due to gravity on moon will be

• A. $0.98m{s}^{-2}$
• B. $0.49m{s}^{-2}$
• C. $9.8m{s}^{-2}$
• D. $4.9m{s}^{-2}$

Answer 1

The correct option is B $0.49m{s}^{-2}$

$g=\frac{GM}{R^2}$
$9.8=\frac{GM}{R^2}$
$g^{\prime }=\frac{GM\times 4}{80\times R^2}$
$=\frac{GM}{R^2}\times \frac{1}{20}$
$=\frac{9.8}{20}$
$g^{\prime }=0.49m{s}^{-2}$.