Acceleration due to gravity on a hypothetical planet.

Classical Mechanics Level 1

Suppose, a hypothetical spherical planet other than the earth has the same density that of the earth and has its radius 3 times that of the earth. What will be the acceleration due to gravity there.

If your answer is (n*g). Where, g is the acceleration due to gravity on the earth. What will ve the value of n ?


The answer is 3.

Snehil Kumar by Snehil Kumar , 24, India

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2 solutions

Parth Sankhe
Dec 20, 2018

r = 3 R r=3R

v = 3 3 V = 27 V v=3^3V=27V , and since density is constant, m = 27 M m=27M

g ′ = G m r 2 = 3 g g'=\frac {Gm}{r^2}=3g

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Snehil Kumar
Dec 20, 2018

Let us assume the radius of the earth and the planet to r and 3r, density be d and the masses be m and M.

Now,

M = d * volume

=> M = d * (4/3) * pi * (3r)^3

=> M = 27m

Now, acceleration due to gravity on earth,

g = Gm/r^2

=> g' = G * (27m) / (3r)^2

=> g' = 3g

=> n = 3

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