Question

2 bodies A and B of masses m and 2m respectively are kept a distance d apart where a small particle replaced , so that the net gravitational force on it due to the bodies A and B is 0.

Answer 1

Question in correct form is:
Two bodies A and B of masses m and 2m respectively are kept a distance d apart. Where a small particle be placed so that the net gravitational force on it due to the bodies A and B is 0.

Answer:
Net gravitational force will be zero towards less massive body.
Let,
The mass of small particle which is being placed is m₀
Distance between m₀ and m = x
Then, distance between m₀ and 2m = d - x

Force due to m on m₀ = Force due to 2m on m₀
Gmm₀/x^2 = G*(2m) * (m₀) / (d - x)^2
1/√2 = x / (d - x)
x√2 = d - x
x = d / 2.414
x = 0.414 d

The small particle should be kept at a distance 0.414d from A.

Answer 2

Question in correct form is:

Two bodies A and B of masses m and 2m respectively are kept a distance d apart. Where a small particle be placed so that the net gravitational force on it due to the bodies A and B is 0.

Answer:

Net gravitational force will be zero towards less massive body.

Let,

The mass of small particle which is being placed is m₀

Distance between m₀ and m = x

Then, distance between m₀ and 2m = d - x

Force due to m on m₀ = Force due to 2m on m₀

Gmm₀/x^2 = G*(2m) * (m₀) / (d - x)^2

1/√2 = x / (d - x)

x√2 = d - x

x = d / 2.414

x = 0.414 d

The small particle should be kept at a distance 0.414d from A.