Question

Two asteroids are located a certain distance away from each other. They have the same mass . The gravitational force of attraction is f . If the mass of one of the asteroids is doubled, how will the gravitational force be affected

Answer 1

Answer:

F' = 2F

Explanation:

The gravitational force of attraction between asteroids is given by Newton's Law of Gravitation:

$F = \frac{Gm_1m_2}{r^2}$

where,

F = Force

G = Universal Gravitational Constant

m₁ = m₂ = m = mass of each asteroid

r = distance between asteroids

Therefore,

$F = \frac{Gm^2}{r^2}$   --------------------- eq(1)

Now, if we double the mass of one asteroid:

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

using equation (1):

F' = 2F