Question

Suppose that two objects attract each other with a gravitational force of 50N. If the mass

of both objects was tripled, and if the distance between the objects was doubled, then what
would be the new force of attraction between the two objects?

Answer 1

F' = 112.5 N

Step-by-step explanation:

The force of gravitation between two objects is given by Newton's Law of Gravitation as follows:

`F = (Gm_(1)m_(2))/(r^2)\\`______________ equation (1)

where,

F = Force = 50 N

G = universal gravitational constant

m₁ = mass of the first object

m₂ = mass of the second object

r = distance between objects

Now, the masses of each object are tripled and the distance between them is doubled:

m₁' = 3m₁

m₂' = 3m₂

r' = 2r

Hence, the new force will be:

`F' = (G(3m_(1))(3m_(2)))/((2r)^2)\\\\F' = (9)/(4)(Gm_(1)m_(2))/(r^2)`

using equation (1), we get:

F' = 2.25 F = 2.25(50 N)

F' = 112.5 N