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

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Solution

Step 1: Given data
Mass of the first body; $m_{1} = 100 k g$
Mass of the second body; $m_{2} = 10000 k g$
Distance between two bodies; $r = 1 m$
Step 2: Formula used
Gravitational field intensity, $E_{g_{}} = \frac{- G M}{R^{2}}$
The unit of gravitational field intensity is N/Kg.
Step 3: Calculation:
Let point O is at a distance of X m from the mass of $100 K g$ .
We need to determine two gravitational forces F₁ and F₂.
Let the intensity of the gravitational field at O is zero, then $F_{1} = F_{2}$
$G \frac{(100)}{x^{2}} = G \frac{(10000)}{{(1 - x)}^{2}}$
After simplification
$X = \frac{1}{11}$
Hence at $X = \frac{1}{11}$ from the smaller body, the intensity of the gravitational field will be zero.

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