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Q.

A body is projected vertically from the surface of Earth with kinetic energy K1 and when it comes
to momentary rest, it is given a horizontal velocity so that its kinetic energy is K2 and it goes into
circular orbit. Then

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a

For escape from surface kinetic energy required is K1+2K2

b

The altitude of the orbit is (K12K2) times radius of earth

c

If initially, the body had been projected horizontally with a kinetic energy of  K12+K1 it would
have gone into circular orbit. 

d

K1>K2

answer is A, B, C.

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Detailed Solution

For escape K.E.=P.E.=K1+2K2

P.E.=2K2(∵=2×KE)

Question Image

GMmR+h=2K2 GMmR=2K2K1

Divide, solve, h=K12K2R

For circular orbit at R,

K.E. required=PE2=2K2+K12

K1  and K2 are independent, cannot be compared

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