Suppose we have two planets with the same mass, but the radius of the second one is twice the size of the first one. How does th

Question

2 years ago

13

e free-fall acceleration on the second planet compare to the first planet

1 answer:

bogdanovich [222] · Answer 1 · 2023-07-12T12:59:06+03:00

The free-fall acceleration on the second planet is one-fourth the value of the first planet.

Calculation:

Consider the mass of planet A to be, M

the mass of planet B to be, Mₓ = M

the radius of planet A to be, R₁

the radius of planet B to be, R₂

The acceleration due to gravity on planet A's surface is given as:

g = GM/R₁² - (1)

Similarly, the acceleration due to gravity on planet B's surface is given as:

g' = GM/R₂² [where, R₂ = 2R₁]

= GM/4R₁² -(2)

From equation 1 & 2, we get:

g/g' = GM/R₁² ÷ GM/4R₁²

g/g' = 4/1

Thus we get,

g' = 1/4 g

Therefore, the free-fall acceleration on the second planet is one-fourth the value of the first planet.

Learn more about free-fall here:

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