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23/01/2022 12:35 pm
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The masses and radii of the earth and moon are (M1, R1) and (M2, R2) respectively. Their centres are at a distance 'r' apart. Find the minimum escape velocity for a particle of mass 'm' to be projected from the middle of these two masses:
(1) V = \(\frac{1}{2}\sqrt{\frac{4G(M_1 + M_2)}{r}}\)
(2) V = \(\sqrt{\frac{4G(M_1 + M_2)}{r}}\)
(3) V = \(\frac{1}{2}\sqrt{\frac{2G(M_1 + M_2)}{r}}\)
(4) V = \(\frac{\sqrt{2G}(M_1 + M_2)}{r}\)
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23/01/2022 12:40 pm
Correct answer: (2) V = \(\sqrt{\frac{4G(M_1 + M_2)}{r}}\)
Explanation:
\(\frac{1}{2}mV^2\) - \(\frac{GM_1m}{\frac{r}{2}}\) - \(\frac{GM_2m}{\frac{r}{2}}\) = 0
\(\frac{1}{2}mV^2\) = \(\frac{2Gm}{r}(M_1 + M_2)\)
V = \(\sqrt{\frac{4G(M_1 + M_2)}{r}}\)