Question

A planet x has a mass 2 times and radius 3 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

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Answer 1

Answer:-

2.22 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.

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∴ 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 = 2Mₑ

∴ Rₚ = 3Rₑ

Hence, expression for acceleartion due to gravity on planet 'X' (gₚ) will be :-

=> gₚ = GMₚ/R²ₚ

=> gₚ = G×2Mₑ/(3Rₑ)²

∴ gₚ = 2GMₑ/9R²ₑ ----(2)

On dividing eq.2 by eq.1, we get :-

=> gₚ/10 = [2GMₑ/9R²ₑ]/[GMₑ/R²ₑ]

=> gₚ/10 = 2/9

=> gₚ = 2×10/9

=> gₚ = 2.22m/s²

Thus, acceleration due to gravity on the planet 'X' is 2.22m/s² .

Answer 2

Let,

Mass of Earth = M

Radius = R

And, we have 'g' in Earth = 10 m/s²

But in Planet X:-

Mass = 2M

Radius = 3R

We know, g = GM/R²

∴ 'g' in Earth = GM/R² = 10 m/s²

In Planet X,

g′ = G(2M)/(3R)² = 2GM/9R² = 2/9 × g = 2/9 × 10 m/s² = 1.11 × 2 m/s²

= 2.22 m/s² {Answer}