Question

Suppose there exist a planet whose mass is half and radius is double than that
of the Earth. What is the ratio of acceleration due to gravity on this planet to
the acceleration due to gravity on the surface of Earth.

Answer 1

The ratio of acceleration due to gravity on the planet and the acceleration due to gravity on the surface of the Earth is 1:8

Step-by-step explanation:

Let the mass of the earth be M and radius R

According to the question, the mass of the planet will be M/2 and radius 2R

We know that

The acceleration due to gravity on the surface of the Earth is given by

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

The acceleration due to gravity on the surface of the planet

$g'=\frac{G(M/2)}{(2R)^2}$

$\implies g'=\frac{GM}{8R^2}$

Ratio

$\frac{g'}{g}=\frac{GM/8R^2}{GM/R^2}$

$\implies \frac{g'}{g}=\frac{1}{8}$

Hope this answer is helpful.

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