There are two bodies of masses 100 kg and

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There are two bodies of masses $100\, kg$ and $10000\, kg $ separated by a distance $1\, m$.  At what distance from the smaller body, the intensity of gravitational field will be zero

A

$\frac{1}{9}\,m$

B

$\frac{1}{{10}}\,m$

C

$\frac{1}{{11}}\,m$

D

$\frac{{10}}{{11}}\,m$

There are two bodies of masses $100\, kg$ and $10000\, kg $ separated by a distance $1\, m$.  At what distance from the smaller body, the intensity of gravitational field will be zero

$\frac{{G \times 100}}{{{x^2}}} = \frac{{G \times 10000}}{{{{(1 - x)}^2}}}$ $ \Rightarrow \,\,\frac{{10}}{x} = \frac{{100}}{{1 - x}}\, \Rightarrow \,x = \frac{1}{{11}}m$