Take the mean distance of the moon and the sun from the earth to be… | JEE Main 2018 (15 Apr, Shift 1)

Q17JEE Main 2018 · 15 APR · SHIFT 1Difficult

Newton's Law of Gravitation

Take the mean distance of the moon and the sun from the earth to be $0.4 \times 10^{6}$ km and $150 \times 10^{6}$ km respectively. Their masses are $8 \times 10^{22}$ kg and $2 \times 10^{30}$ kg respectively. The radius of the earth is $6400$ km. Let $\Delta F_1$ be the difference in the forces exerted by the moon at the nearest and farthest points on the earth and $\Delta F_2$ be the difference in the force exerted by the sun at the nearest and farthest points on the earth. Then, the number closest to $\frac{\Delta F_1}{\Delta F_2}$ is:

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Answer: (a)

Difference between near and far points: $\Delta F \approx \frac{GMm}{d^3}\cdot 2(2R_e)$ , so $\Delta F \propto \frac{M}{d^3}$ .
$\frac{\Delta F_1}{\Delta F_2} = \frac{M_m}{M_s}\left(\frac{d_s}{d_m}\right)^3 = \frac{8 \times 10^{22}}{2 \times 10^{30}}\left(\frac{150}{0.4}\right)^3$
$= 4 \times 10^{-8} \times 375^3 = 4 \times 10^{-8} \times 5.27 \times 10^{7} \approx 2.1$
So the answer is (a) 2.

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Newton's Law of Gravitation question from JEE Main 2018 (15 Apr, Shift 1)

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