Question

If the acceleration due to gravity g at the earth's surface is $9.8m{s}^{-2}$, mass of the earth $80$ times that of moon and radius of the earth $4$ times that of the moon, then the value of g at the moon's surface will approximately be :

• A. $4m{s}^{-2}$
• B. $1.96m{s}^{-2}$
• C. $27m{s}^{-2}$
• D. $16m{s}^{-2}$

Answer 1

The correct option is B $1.96m{s}^{-2}$

Here, the acceleration at the earth's surface is $g=g_e=\frac{G{M}_e}{R_e^2}$ and the acceleration at the moon's surface is $g_m=\frac{G{M}_m}{R_m^2}$

Here, $M_e=80M_m$ or $M_e/M_m=80$ and $R_e=4R_m$ or $R_e/R_m=4$

So, $\frac{g_m}{g_e}=\left(M_m/M_e\right)(R_e/R_m{)}^2=(1/80\left)\right(4{)}^2=0.2$

or $g_m=0.2g=0.2\left(9.8\right)=1.96m/s^2$