Question

If mass of one object is increased by 3 times and mass of other object is increased by 8 times (keeping distance of separation constant), then gravitational force between them-

Increases by 11 times

Decreases by 11 times

Increased by 24 times

Does not change at all​

Answer 1

Answer:-

Increased by 24 times

Explanation:-

According to Newton's Universal Law of Gravitation, we know that:-

=> F = GMm/r² ----(1)

Where:-

• F is the gravitational force.

• G is Universal Gravitational Constant

• M is mass of the 1st body

• m is mass of the 2nd body

• r is the distance between the bodies

Now, as per as given condition, when mass of one object is increased 3 times i.e. 3M and mass of another object is increased 8 times i.e. 8m, then new gravitational force [F'], will be :-

=> F' = G×3M×8m/r²

=> F' = 24GMm/r² ----(2)

On dividing eq.2 by eq.1, we get :-

=> F'/F = [24GMm/r²]/[GMm/r²]

=> F'/F = 24

=> F' = 24F

Thus, it is clear that the new gravitational force is increased by 24 times.

Answer 2

Let,

Mass of 1st object = M

Mass of 2nd object = m

Distance between them = d

∴ F = GMm/d²

But here,

Mass of 1st object = 3M

Mass of 2nd object = 8m

Distance = d

∴ F = G(3M)(8m)/d² = 24GMm/d² = 24F {Answer}

So, (iii) Increases by 24 times – correct option.