A planet x has a mass 3 times and radius 6 times that of the Earth. What is the acceleration due to gravity on the planet, if the acceleration due to gravity on the Earth is 10 m/s2.
Answers
Answer:
Answer:-
0.83 m/s²
Explanation:-
We know that :-
gₑ = GMₑ/R²ₑ
Where :-
• gₑ is the acceleration due to gravity on
the earth's surface.
• G is Universal Gravitational Constant.
• Mₑ is mass of the earth.
• Rₑ is radius of the earth.
_____________________________
∴ 10 = GMₑ/R²ₑ ----(1)
Now according to the question, mass of planet 'X' is 2 times that of earth and radius of the planet is 3 times that of earth.
∴ Mₚ = 3Mₑ
∴ Rₚ = 6Rₑ
Hence, expression for acceleartion due to gravity on planet 'X' (gₚ) will be :-
=> gₚ = GMₚ/R²ₚ
=> gₚ = G×3Mₑ/(6Rₑ)²
∴ gₚ = 3GMₑ/36R²ₑ ----(2)
On dividing eq.2 by eq.1, we get :-
=> gₚ/10 = [3GMₑ/36R²ₑ]/[GMₑ/R²ₑ]
=> gₚ/10 = 3/36
=> gₚ = 3×10/36
=> gₚ = 0.83m/s²
Thus, acceleration due to gravity on the planet 'X' is 0.83m
Explanation: