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Q.

A projectile is projected with velocity kve in vertically upward direction from the ground into the space. (ve is escape velocity and k < 1). If air resistance is considered to be negligible, then the maximum height from the centre of earth to which it can go will be (R = radius of earth)

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a

Rk2+1

b

Rk2−1

c

R1−k2

d

Rk+1

answer is C.

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Detailed Solution

Kinetic energy = Potential energy12mkve2=mgh1+hR⇒12mk22gR=mgh1+hR⇒h=Rk21−k2Height of projectile from the earth's surface = hHeight from the centre, r=R+h=R+Rk21−k2By solving, we get r=R1−k2
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