Question

The gravitational force between two identical bodies is 200 N. Mass of both the bodies becomes twice and separation becomes half. What will be new force between them?​

Answer 1

Answer:The force becomes 16 times i.e 16 × 200 = 3200N

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Answer 2

Given :

Gravitational Force (F) = 200 N

To Find :

What will be new force when the mass of both the bodies becomes twice and separation becomes half.

Solution :

We know, Every body in the universe pulls every other body with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

The Gravitational force (F) formula is given by -

 F = $\frac{Gm_1m_2}{r^2}$

Where, G = Gravitational constant; m₁ and m₂ = mass of the bodies; r = Distance between the bodies.

Given m₁ = m₂

Let m₁ = m₂ = m (say)

Gravitational force (F) =  $\frac{Gm^2}{r^2}$  =  200 N

Now, the gravitational force when the mass of both the bodies becomes twice and separation becomes half -

    F' = $\frac{G * 2m * 2m}{(r/2)^2}$

        = 16 × $\frac{Gm^2}{r^2}$

        = 16 × 200

        = 3200 N

Therefore, the force acting between the bodies when the mass of both the bodies becomes twice and separation becomes half is 3200 N.