Consider a planet moving in an elliptical orbit round the sun. The work done on the planet by the gravitational force of the sun
A. Is zero in any small part of the orbit.
B. Is zero in some parts of the orbit.
C. Is zero in one complete revolution
D. Is zero in no part of the motion.
The work done is equal to the dot product of force times displacement. If the force is perpendicular to the direction of displacement, then the work done is zero. In elliptical orbits, this situation occurs at the apogee and perigee points. Hence, option (b) is true and (d) is false. In rest of the points, the force makes an angle with displacement and hence, work done is not zero. Therefore, (a) is false. In one complete revolution, the total displacement is zero. Hence the work done is zero and (c) is true.
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