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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Solution

We have to find distance x, so that the net force acting on 1 kg body is equal to zero.
The force applied by 10 kg body on 1 kg body will be towards 10 kg body and that applied by 5 kg body on 1 kg body will be towards 5 kg body.
These forces should be equal and opposite.
$G \times \frac{5 \times 1}{x^{2}} = G \times \frac{10 \times 1}{2^{2}}$
$\frac{5}{x^{2}} = \frac{5}{2} \Rightarrow x^{2} = 2$
$\Rightarrow x = 2^{\frac{1}{2}} = 1.414 m$
The 5 kg body should be kept at 1.414 m from 1 kg body.

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