Question

The mass of earth is 80 times that of moon and their diameters are in the ratio 4:1 respectively.
What is the value of g on moon if g on earth $9.8m/s^2$.

Answer 1

Suppose $R_e$ be radius of the earth and $R_m$ be that of the moon. so according question $R_e=4R_m$

And if $M_e$ be the mass of the earth and $M_m$ is the mass of the moon then $M_e=80M_m$

Value of g on the moon is $g_m=G{M}_m/R_m^2$...............(1)

Value of g on the earth is $g_e=G{M}_e/R_e^2=\frac{G\times 80M_m}{16\times R_m^2}=\frac{5G{M}_m}{R_m^2}=5g_m$

So value of g on moon is $g_e/5=9.8/5=1.96m/s^2$