Question

The gravitational force between two objects is F. If masses of both the objects are halved without altering the distance between them, the gravitational force would become
The gravitational force between two objects is F. If masses of both the objects are halved without altering the distance between them, the gravitational force would become *

F/4
F/2

F
2F​

Answer 1

Answer:

Explanation:

Gravitational force between two objects varies directly as their masses and inversely as the square of the distance between them. So, when the masses of both objects are halved without changing the distance, the gravitational force between them would become one-fourth of the original value.

so the correct option is

F/4

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Answer 2

Answer:-

Let the mass of first body be M and mass of second body be m.

Given:

Gravitational force between them = F.

We know that,

Gravitational force (F) = GMm/r²

[ where r is the Distance between them and G is the gravitational constant. ]

So,

⟶ F = GMm/r² -- equation (1)

Now,

Their masses are halved.

• mass of first body = M/2

• mass of second body = m/2

Let ,

Gravitational force between them = F'

⟶ F' = G(M/2)(m/2) / r²

⟶ F' = (GMm/4) * 1/r²

⟶ F' = (GMm/r²) * (1/4)

⟶ F' = F * 1/4

[ from equation (1) ]

⟶ F' = F/4

∴ The gravitational force between them reduces to F/4 when the masses of objects are halved.