Question
A body projected vertically from the earth reaches a height equal to earth's radius before returning to the earth. The power exerted by the gravitational force is greatest

Answer

Power, hitting $P=  \vec F\cdot \vec v  = 0 = Fv\cos\theta $
Just before hitting the earth $\theta =0^o$ Hence, the power exerted by the gravitational force is greatest at the instant just before the body hits the earth. 

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