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 (a) at the highest position of the body (b) at the instant just before the body hits the earth. (c) it remains constant all through. (d) at the instant just after the body is projected.

Answer: (b). Power of gravity P = F · v = mgvcos θ. Speed is largest at the earth's surface (and g is also largest there). Just after projection v is opposite to gravity, so P is negative; just before hitting, v is along gravity, so P is maximum positive. So the answer is (b).

A body projected vertically from the earth reaches a height equal to… | NEET 2011 (AIPMT, Prelims)

Q42NEET 2011 · AIPMT · PRELIMSMedium

Power

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

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Answer: (b)

Power of gravity $P = \vec{F} \cdot \vec{v} = mgv\cos\theta$ .
Speed is largest at the earth's surface (and $g$ is also largest there).
Just after projection $\vec{v}$ is opposite to gravity, so $P$ is negative; just before hitting, $\vec{v}$ is along gravity, so $P$ is maximum positive.
So the answer is (b).

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