Question

What will be the acceleration due to gravity on the surface of the moon, if its radius is $1/4^{th}$ the radius of the earth and its mass is $1/80$ times the mass of the earth.

Answer 1

The acceleration due to gravity is: $\frac{GM}{r^2}$ where G is constant

M affects the result by direct proportion and r by inverse square proportion.Reducing the radius by four, increases by 16 times.Reducing the mass of factor of 80 reduces the result by same factor.

The final result is $\frac{16}{80}$ = $\frac{1}{5}$. Hence the surface acceleration on the moon is 0.2g.