Question

5. A body of mass 1 kg is placed at a distance of 2 m from another body of mass 10 kg. At what distance from the
body of mass 1 kg, another body of mass 5 kg must be placed so that the net gravitational force acting on the
body of mass 1 kg is zero?

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Answer 1

Answer:

Distance of null point from 1kg = x

Null point lies between 5kg and 10kg

F1 = F2

GMm / x^2 = GM’m / (2 + x)^2

Divide both sides by Gm

M / x^2 = M’ / (2 + x)^2

5 / x^2 = 10 / (2 + x)^2

2x^2 = 2^2 + x^2 + 4x

x^2 - 4x - 4 = 0

Solve the above quadratic equation

x = 2(1 + √2)

x = 4.828 m

5kg should be placed at a distance of 4.828 m from 1kg

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