Question

For moon its mass is $\frac{1}{81}$ of earth's mass and its diameter is $\frac{1}{3.7}$ of earth's diameter. If acceleration due to gravity of earth surface is $9.8m/s^2$, then at moon its value is

• A. $2.86m/s^2$
• B. $1.65m/s^2$
• C. $8.65m/s^2$
• D. $5.16m/s^2$

Answer 1

The correct option is B $1.65m/s^2$

Acceleration due to gravity ,
$g=\frac{{GM}_e}{R^2}Atearth,g_e=\frac{{GM}_m}{r_e^2},andatmoon{g}_m=\frac{{GM}_m}{R_m^2}\therefore \frac{g_e}{g_m}=\frac{M_e}{M_m}{\left(\frac{R_e}{R_m}\right)}^2\Rightarrow g_m=g_e\times \frac{M_m}{M_e}\times {\left(\frac{R_e}{R_m}\right)}^2=9.8\times \frac{1}{81}\times 3.7\times 3.7=1.65meter/{sec}^2$