Question

Two planets have radii r and 2r have densities d and 4d respectively. Find the ratio of their acceleration due to gravity.
Give full solution.

a) 1:2

b) 2:3

c) 1:8

d) 2:5

Answer 1

Hope it will help you.

Answer 2

SOLUTION:

We know, d = M/V

              => mass = density x volume

Now,  let volume of planet 1 = 4/3 πr^3 = k

Therefore, mass of planet 1 = k x d

Again volume of planet 2 = 4/3 π(2r)^3

                                          = 8 x k

Then, mass of planet 2 = 8k x 4d

Now, g = GM/R^2

Therefore, g1 = G x kd/r^2

         And, g2 =  G x 32kd /4r^2

FInally, g1 : g2 = 1 : 8

Hence, Answer is (C).