Respuesta :
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 :
[tex]g=G\dfrac{M}{r^2}[/tex]
G is universal gravitational constant
M is mass of Earth and r is radius of Earth
Let [tex]g'[/tex] is the acceleration due to gravity on the surface of planet X. So,
[tex]g'=G\dfrac{M'}{r'^2}[/tex] .......(1)
M' is the mass of planet X and r' is the radius of planet X.
So,
[tex]2.95g=G\dfrac{M'}{(3.5r)^2}[/tex] .....(2)
Dividing equation (1) and (2) we get :
[tex]\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[/tex]
So, the mass of planet X is 36.23 times that if earth.
