Applying energy conservation from ((1)to(2),
21m⋅(Re2GM)−ReGMm=21mv2−R+rGMm
⇒21mv2=R+rGMm
⇒v=R+r2GM=dtdr
⇒2GM∫0tdt=∫ReRe+h(R+r)dr
2GM⋅t=32[(R+r)23]ReRe+h
t=322GMRe3[(1+Reh)23−1]
Re2GM=g
t=31g2Re[(1+Reh)23−1]
A body is projected vertically upwards from the surface of earth with a velocity sufficient enough to carry it to infinity. The time taken by it to reach height h is S.
Held on 22 Jul 2021 · Verified 6 Jul 2026.
2gRe[(1+Reh)23−1]
g2Re[(1+Reh)23−1]
312gRe[(1+Rch)23−1]
31g2Rc[(1+Reh)23−1]
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