Question

The force of gravity between Tim and John is 1.85 x 10^-9 N. If they are 18 m apart and Tim has a mass of 120 kg, what is John’s mass ?

Answer 1

75kg

Step-by-step explanation:

Given:

Force of gravity(F) = 1.85 x 10⁻⁹N

distance between Tim and John = 18m

Mass of Tim = ?

Unknown:

Mass of John = ?

Solution

Newton's law of universal gravitation states that every particle of matter in the universe attracts every other particle with a force that is directly proportional to the product of the masses of the particles and inversely proportional to the square of the distance between them.

i.e

F =G
`(m_(1) m_(2))/(r^(2) )`

let

m₁ represent mass of Tim

m₂ mass of John

G is the universal gravitation constant = 6.67 x 10⁻¹¹Nm²kg⁻²

r is the distance seperating them

The unknown is m₂ and we should make it the subject of the expression:

m₂ = F
`(r^(2) )/(m_(1) )` x
`(1)/(G)`

m₂ =
`(1.85 x 10^(-9)  x  18^(2)  )/(G x 120)`

m₂ = 75kg