Question

6) Two small balls, A and B, attract each other gravitationally with a force of magnitude F. If we now double both masses and the separation of the balls, what will now be the magnitude of the attractive force on each one?

Answer 1

Answer:

The magnitude of the attractive force is unchanged

Explanation:

Newton's Law of Universal Gravitation: The law states that the force of attraction between two mass m₁ and m₂ is directly proportional to the product of the masses and inversely proportional to the square of the distance (d) between them.

Mathematically it is represented as

F = Gm₁m₂/d₂ ............................. Equation 1

Where G = universal Constant, F = Force of attraction or repulsion, m₁ = mass of the first body,  m₂ = mass of the second body, d = distance between the masses.

When both masses and the separation of the ball are doubled,

I.e

Fₙ = G(2m₁)(2m₂)/(2d)²

Where Fₙ = the new gravitational force, when both masses and distance are separation are doubled.

Fₙ = 4Gm₁m₂/4d²

Fₙ = Gm₁m₂/d²........................... Equation 2

Comparing Equation 1 and equation 2,

Fₙ = F

Therefore the magnitude of the attractive force between the balls when their masses and separation are doubled remains the same.

I.e The magnitude of the attractive force is unchanged,