Question

The distance between two bodies becomes 6 times more than the
usual distance. Then the force F becomes
a) 36 times b)6 times c)12 times d) 1/36 TIMES

Answer 1

Answer:-

The force,F becomes 1/36 times [Option.d]

Explanation:-

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

F = GMm/r². -----(1)

Where :-

• F is the gravitational force between

the bodies.

• G is Universal Gravitational Constant.

• M is mass of the 1st body.

• m is mass of the 2nd body.

• r is the distance of separation between

the bodies.

Now according to given condition, the distance of separation between the bodies becomes 6 times more than the usual distance i.e 6F. So, the equation for new gravitational force (F') will be :-

=> F' = GMm/(6r)²

=> F' = GMm/36r². ----(2)

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

=> F'/F = [GMm/36r²]/[GMm/r²]

=> F'/F = 1/36

=> F' = F/36

Thus, the force is decreased by 36 times i.e. 1/36.

Answer 2

Let,

Mass of one object = M

Mass of the second one = m

Distance between them = d

∴ F = GMm/d²

But here,

Mass of both the objects are same.

But, distance = 6d

⇒F′ = GMm/(6d)²

= GMm/36d²

= 1/36(GMm/d²)

= F/36 (D).