A space craft from the earth is moving towards the moon, find a location from the earth where at the gravitational force is zero. [Mass of the earth = 6 x 10²⁴ kg, Mass of the moon = 7.4 x 10²² kg, distance between the earth and the moon = 3.8 x 10⁸ m]

Question

Accepted Answer

খ. 3.42 x 10⁸ m

ব্যাখ্যা: পৃথিবী থেকে $x$ দূরত্বে মহাকর্ষ বল শূন্য হলে:
$\frac{G M_e m}{x^2} = \frac{G M_m m}{(d - x)^2}$
$\implies \frac{d - x}{x} = \sqrt{\frac{M_m}{M_e}} = \sqrt{\frac{7.4 	imes 10^{22}}{6 	imes 10^{24}}} = \sqrt{0.012333} \approx 0.111$
$\implies \frac{d}{x} = 1 + 0.111 = 1.111$
$\implies x = \frac{d}{1.111} = \frac{3.8 	imes 10^8}{1.111} \approx 3.42 	imes 10^8	ext{ m}$।

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