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Q.

A ball of mass m is fired vertically upward from the surface of the earth with velocity nvewhere ve is the escape velocity and n < 1. Neglecting air resistance, to what height will the ball rise ? Take radius of the earth as R

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a

R/n2

b

R/1−n2

c

Rn2/1−n2

d

Rn2

answer is C.

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Detailed Solution

According to this problem12mv2=GMmR−GMm(R+h)=GMmhR(R+h)=mgh(R+h) ∵g=GMRFurther 12mv2=12mn2ve2=12mn2(2gR) ∵ve=2gR∴ 12mn2(2gR)=mgh(R+h)Solving, we get h=Rn2/1−n2
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A ball of mass m is fired vertically upward from the surface of the earth with velocity nvewhere ve is the escape velocity and n < 1. Neglecting air resistance, to what height will the ball rise ? Take radius of the earth as R