Question

If the ratio of the mass of the planet A and planet B is 2:3 while their ratio of the radius of the planet A and planet B is 1:2 If the weight an object on planet A is w what is the weight of object on B

Answer 1

Given ratio of their masses

2 : 3


Let the mass be 2m and 3m respectively.

Mass of planet A = 2m
And that of B = 3m

Similarly, let the radius of A be r and therefore, radius of B = 2r


Now weight = mass of obj × g

So we have to find the value of g on both planets.


g = GM/R²

Where G = gravitational constant, M = mass of planet, R = radius of planet

For A, g = G2m/r²

Now weight = mass of object × g

Let the mass of object be y

=> weight = y × G2m/r²

Given weight = w

=> w = yG2m/r²

Now g of planet B = G3m/(2r)²

=> g of planet B = G3m/4r²


Now, gA/gB = G2m/r² ÷ G3m/4r²

=> gA/gB = G2m/r² × 4r²/G3m

=> gA/gB = 2 × 4

=> gA/gB = 8

=> gA = 8 times of gB

=> gB = 1/8 × gA


So weight of object on B = mass of obj × gB

=> y × 1/8 × gA

=> y × gA × 1/8

=> y × G2m/r² × 1/8

=> w × 1/8

(since, y × G2m/r² = w)

= w/8


Your answer :- w/8