Question

4. The gravitational force between two objects is 100 N. How should the distance between these objects be changed
so thar the force between them becomes 50 N ?
(C.B.S.E. 2015) [Ans. Vr]​

Answer 1

Answer:-

Given:

Gravitational force between two objects (F) = 100 N.

We know that,

F = GMm/r²

Where,

• G is gravitational constant

• M is mass of first object

• m is mass of second Object

• r is distance between them.

Hence,

→ GMm/r² = 100 N

⟶ GMm = 100r² -- equation (1).

Now,

We have to find the change in distance between them.

That is: relation between original distance & new distance.

Let the new distance be r'.

Hence,

⟶ GMm/(r')² = 50

Putting the value of GMm from equation (1) we get,

⟶ 100r²/(r')² = 50

⟶ 100r² = 50 * (r')²

⟶ 100 * r² / 50 = (r')²

⟶ (10 * r/5√2)² = (r')²

⟶ 10r/5√2 = r'

⟶ √2 * r = r'

Therefore, the gravitational force between the objects becomes 50 N if the distance becomes √2 times it's original value.