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 $9.8$ $m{s}^{-2}$ then the value of acceleration due to gravity on moon will be?

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

Answer 1

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

Given Mass of earth =80 Mass of moon and diameter of earth = 2 diameter of moon and acceleration due to gravity o earth= 9.8 $\text{m}/s^2$

From the formula of acceleration due to gravity

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

Now dividing the acceleration due to gravity of moon to acceleration due to earth we get

$\frac{g_M}{g_E}=\frac{\frac{G{M}_M}{R_M}}{\frac{G{M}_E}{R_E}}=\frac{4}{80}{g}_M=\frac{9.8}{20}=0.49m/s^2$