Question

The acceleration of gravity on the surface of planet X is 2.95 times the acceleration of gravity on the surface of Earth and the radius of planet X is 3.5 times the radius of Earth. What is the mass of planet X?

Answer 1

Answer:

The mass of planet X is 36.23 times that if earth.                                  

Explanation:

Given that,

The acceleration of gravity on the surface of planet X is 2.95 times the acceleration of gravity on the surface of Earth and the radius of planet X is 3.5 times the radius of Earth

The formula of acceleration due to gravity is given by :

$g=G\dfrac{M}{r^2}$

G is universal gravitational constant

M is mass of Earth and r is radius of Earth

Let $g'$ is the acceleration due to gravity on the surface of planet X. So,

$g'=G\dfrac{M'}{r'^2}$  .......(1)

M' is the mass of planet X and r' is the radius of planet X.

So,

$2.95g=G\dfrac{M'}{(3.5r)^2}$  .....(2)

Dividing equation (1) and (2) we get :

$\dfrac{g}{2.95g}=\dfrac{M}{M'}\times \dfrac{(3.5r)^2}{r^2}\\\\\dfrac{1}{2.95}=\dfrac{M}{M'}\times 12.25\\\\\dfrac{M}{M'}=\dfrac{1}{2.95\times 12.25}\\\\\dfrac{M}{M'}=0.027\\\\M'=36.23\ M$

So, the mass of planet X is 36.23 times that if earth.