The mass of a ball if four times the mass of another ball. When these balls are separated by a distance of 10 cm, the gravitational force between them is `6.67xx10^(-7)N`. Find the masses of the two balls.

Explanation

Mass of 1st ball =m
Mass of 2nd ball =4m
Separation, `r= 10 cm= 0.1` m
Mass of the 1st ball = m=?
Gravitation force, `F=6.67xx10^(-7) N`
Gravitational force, `F=(G*m*4m)/(r^2)`
`implies 6.67xx10^(-7)= (6.67xx10^(-11)4m^2)/(0.1xx0.1)`
`implies 10^(-7)=10^(-9).4m^2`
`:. m^2=(10^(-7))/(4xx10^(-9)) =(100)/(4)= 25 implies m=5`
Mass of the balls are 5kg, 20kg.