A ball of mass m is fired vertically upwards from the surface of the earth with velocity nve where ve is the escape velocity and n > 1. To what height will the ball rise? Neglecting, air resistance, take radius of the earth as R
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a
Rn2
b
R1−n2
c
Rn21−n2
d
Rn2
answer is C.
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Detailed Solution
12mv2=GMmR−GMmR+h=GMmhR(R+h)=mghRR+h Since v=nve and ve=2gR, hence, h=Rn21-n2