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MHT CET 2020 (16 Oct, Shift 1) · Gravitational Field

Gravitational Field question from MHT CET 2020 (16 Oct, Shift 1)

Q8MHT CET 2020 · 16 OCT · SHIFT 1Medium

Gravitational Field

The mass of earth is 81 times the mass of the moon and the distance between their centres is $R$ . The distance from the centre of the earth, where gravitational force will be zero is

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Answer: (c)

At the null point the pulls of earth and moon are equal: $\frac{GM_e}{x^2} = \frac{GM_m}{(R-x)^2}$ , with $x$ from the earth's centre.
$\frac{x}{R-x} = \sqrt{\frac{M_e}{M_m}} = \sqrt{81} = 9$
$x = 9R - 9x \Rightarrow x = \frac{9R}{10}$
So the answer is (c) $\frac{9R}{10}$ .

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