There are two bodies of masses $10^{3}$ kg and $10^{5}$ kg separated by a distance of $1$ km. At what distance from the smaller body, the intensity of gravitational field will be zero?

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Solution

The correct option is B $1 / 11$ km
$\frac{G \times 10^{3}}{(r)^{2}} = \frac{G \times 10^{5}}{(1 - r)^{2}}$
$\frac{1}{r^{2}} = \frac{10^{2}}{(1 - r)^{2}}$
$\frac{1}{r} = \frac{10}{1 - r} \Rightarrow 10 r = 1 - r$
$∵ r = \frac{1}{11}$ km

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There are two bodies of masses 103kg and 105kg separated by a distance of 1 km. At what distance from the smaller body, the intensity of gravitational field will be zero?

The correct option is B 1/11 kmG×103(r)2=G×105(1−r)21r2=102(1−r)21r=101−r⇒10r=1−r∵r=111 km

There are two bodies of masses $10^{3}$ kg and $10^{5}$ kg separated by a distance of $1$ km. At what distance from the smaller body, the intensity of gravitational field will be zero?

The correct option is B $1 / 11$ km
$\frac{G \times 10^{3}}{(r)^{2}} = \frac{G \times 10^{5}}{(1 - r)^{2}}$
$\frac{1}{r^{2}} = \frac{10^{2}}{(1 - r)^{2}}$
$\frac{1}{r} = \frac{10}{1 - r} \Rightarrow 10 r = 1 - r$
$∵ r = \frac{1}{11}$ km