Question

Two objects of mass 3M and 3m/2 separated by distance r/4 having the gravitational force F. If first mass gets doubled and second mass gets tripled and distance between them gets half what will be the new gravitational force​

Answer 1

Answer:

The new gravitational force will be 12 times of old gravitational force.

Explanation:

Case I:

Given,

Two masses of Two Objects are M₁ = 3M and

                            M₂ = 3M/2

the distance between the two objects is, R = r/4

Then, the gravitational force F₁ = GM₁M₂/${R_{1}} ^{2}$ = G$M^{2}$/${R_{1}} ^{2}$

Now, Case II:

Given,

Two masses of Two Objects are M₁ = 3M x 2 = 6M

                                                      M₂ = 3M/2 x 3 = M/2

                                            and    R₂ = R₁/2

Then, the gravitational force will be F₂ = GM₁M₂/${R_{2}} ^{2}$

                                                               = (G x 6M x M/2) ÷ $[R_{1}/2] ^{2}$

                                                               = 12G$M^{2}$/${R_{1}} ^{2}$

Therefore, the F₂ = 12 x F₁

Thus, the new gravitational force is 12 times of old gravitational force.