Question

The gravitational force between two objects are 200n .. how should the distance between the two be changed so that force become 100n

Answer 1

it must be increased by root 2 times

Answer 2

We have to find the distance between them be changed so that force becomes 100 N. if initial gravitational force between two object is 200N.

According to Newton's law of Gravitation,

“If two object of mass m and M are separated r distance from each other, the force acting between them is given by,

$F=\frac{GmM}{r^2}$

let r is the initial distance and r' is final distance between them.

initial force, F = 200N = (GmM)/r² ...(1)

final force, F' = 100N = (GmM)/(r')² ...(2)

from equations (1) and (2) we get,

⇒ 100 × (r')² = 200 × r²

⇒(r')² = 2 × r²

⇒r' = √2r

Therefore change in distance between them should be √2 times of its initial distance so that force becomes 100N.