Question

two bodies A and B of mass m1 and 2m respectively are kept at a distance d where should a small particle kept so the net gravitation force on it due to the bodies is 0 then find distance between small particle and body A

Answer 1

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gd morning

here is your 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.

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Answer 2

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♪＼(*＾▽＾*)／＼(*＾▽＾*)／

Net gravitational force = zero

The mass of small particle which is being placed is m₀

Distance between m₀ and m = x

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 must be kept at distance ‼‼‼0.414d‼‼‼ from A✴➖✴

thank you ☺