Two spherical balls of 1 kg and 4kg are seprated by a distance of 12 cm. Find the distance of a point from the 1 kg mass at which the gravitational force on any mass becomes zero.

Explanation

Mass, `m_1=1kg` ,Mass, `m_2=4kg`
Separation, d=12 cm
Mass of 3rd body `m_3`=?

For `m_3` not to experience any force the condition is
Force between `m_1,m_3`= Force berween `m_2,m_3`
`:. (G_1xxm_3)/(x^2)=(Gxx4m_3)/((d-x)^2) implies (d-x)^2=4x^2`.
Take square roots on both sides.
`d-x=2x implies d=3x` or `x=(12)/(3)=4` cm
Distance from 1 kg mass =4 cm.