Question

v= √8πGρ/3 prove answer this ques jaldi please​

Answer 1

Answer:

your solution is as follows

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Step-by-step explanation:

$to \: prove \: that : \\ escape \: velocity \: of \: earth = \\ R. \sqrt{ \frac{8G\piρ}{3} } \\ \\ we \: know \: that \\ earth \: is \: an \: oblate \: spheroid \\ therefore \: so \: \\ volume \: of \: earth = volume \: of \: sphere \\ v= \frac{4}{ 3} \pi.R {}^{3} \: \: \: \: (1) \\ \\ we \: know \: that \\ density = \frac{ mass}{volume} \\ \\ ρ = \frac{M}{v} \\ \\ M = ρv \\ M = \frac{4}{3} \pi.R {}^{3} .ρ \: \: \: \: \: \: \: \: from \: (1)$

$we \: have \\ escape \: velocity \: of \: earth \: = \: \sqrt{ \frac{2GM}{R} } \\ \\ = \sqrt{ \frac{2G}{R} \times M } \\ \\ = \sqrt{ \frac{2G}{R} \times \frac{4}{3}\pi.R {}^{3} } \\ \\ = \sqrt{ \frac{8Gρ.\pi.R {}^{2} }{3} } \\ \\ = R . \sqrt{ \frac{8G\pi.ρ}{3} }$