Question

Two particles are placed at some distance. If the mass of each of the two particles is doubled,

keeping the distance between them unchanged, the value of gravitational force between them will be​

Answer 1

Answer:

Let the masses be denoted as m₁ & m₂.

r is the distance between them.

Gravitational force between them = Gm₁m₂/r²

Now, if masses are doubled,

2m₁ and 2m₂

Gravitational force between them = G.2m₁.2m₂/r²

= G[2(m₁m₂)]/r²

I Hope This Helps.

Answer 2

Solution:

According to Newton's law of gravitation,

$\dag \: \boxed{\sf{F = Gm_1m_2/r^2}}$

here,

• F = gravitational force
• m₁ , m₂ = m = mass
• r = distance between the two masses

⇒ F = G x m x m / r ²

⇒ F = G m² / r² ...(1)

Now,

A per the given condition,

• m₁ = 2m
• m₂ = 2m
• Distance between the two masses remains unchanged ( r)

Hence,

⇒ F' = G x 2m x 2 m / r ₂

⇒ F' = 4x Gm² / r²

⇒ F' = 4F  ...(From 1)

The value of the new gravitational force will be 4F.