Two particles of masses `9M` and `16M` are placed at separtion `d`. At what distance from `9M`, gravitational field is zero.

Explanation

Let gravitational field is zero at distance `x` from `9m`. Gravitational field at `P`
Due to `9M,E_(1)=(G.9M)/(x^(2))`, along `PA`
Due to `16M,E_(2)=(G.16M)/((d-x)^(2))`, along `PB`
Since gravitational field at `P` is zero
`E_(1)=E_(2)`
`(9GM)/(x^(2))=(16GM)/((d-x)^(2))`
Taking square root
`3/x=4/((d-x)) implies 3d-3x =4x`
`x=3d//7`