The mass of a ball is four times the mass of another ball. When these balls are separated by a distance of 1 0 cm, the force of gravitation between them is `6.67 xx 10^(-7)`N. Find the masses of the two balls.

Explanation

`m_1 = m, m_2 = 4m, d=10 cm = 10 xx 10^(-2) m,`
`F = 6.67 xx 10^(-7) "N"`
`G = 6.67 xx 10^(-11) "Nm"^(2) // "kg"^(2)`
`F = (G m_1 m_2)/( d^2)`
`6.67 xx 10^(-7) = (6.67 xx 10^(-11) xx m xx 4m)/( (10 xx 10^(-2) )^2)`
`4m^(2) = 10^(2)`
`m^(2) = (100)/(4) = 25`
`m = 5 "kg"`
`therefore m_1 = m= 5 kg`
`m_2 = 4m = 4 xx 5 = 20 "kg"`