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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 instant just after the body is projected
B
At the highest position of the body
C
At the instant just before the body hits the earth
D
It remains constant all through
Detailed Solution
Power delivered by a force is $P = \vec{F}\cdot\vec{v} = Fv\cos\theta$
Just after projection, the velocity is upward and gravity is downward, so $\theta = 180^\circ$ and the power is negative.
At the highest point, v = 0, so the power is zero.
Just before the body hits the earth, the velocity is downward, i.e., along the force ($\theta = 0^\circ$, $\cos\theta = 1$).
At that instant the speed is maximum and the gravitational force is also maximum (the body is nearest to the earth), so $P = Fv$ is the greatest.
Hence the power is greatest at the instant just before the body hits the earth.
Just after projection, the velocity is upward and gravity is downward, so $\theta = 180^\circ$ and the power is negative.
At the highest point, v = 0, so the power is zero.
Just before the body hits the earth, the velocity is downward, i.e., along the force ($\theta = 0^\circ$, $\cos\theta = 1$).
At that instant the speed is maximum and the gravitational force is also maximum (the body is nearest to the earth), so $P = Fv$ is the greatest.
Hence the power is greatest at the instant just before the body hits the earth.