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

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

Step-by-step 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(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(M')/(r'^2)` .......(1)

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

So,

`2.95g=G(M')/((3.5r)^2)` .....(2)

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

`(g)/(2.95g)=(M)/(M')* ((3.5r)^2)/(r^2)\\\\(1)/(2.95)=(M)/(M')* 12.25\\\\(M)/(M')=(1)/(2.95* 12.25)\\\\(M)/(M')=0.027\\\\M'=36.23\ M`

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