Question

A planet is 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 no part of the motion
(b) is zero in some parts of the orbit
(c) is zero in one complete revolution
(d) is zero in any small part of the orbit

• A. only (c) is true
• B. only (b), (c), (d) are true
• C. only (b) and (c) are true
• D. only (a) is true

Answer 1

Answer: (C)

Gravitational force is a conservative force,
hence work done in a complete cycle will be zero due to zero displacement.
Again, since, work done, $W=F\cdot dr=ma\cdot dr$
If $a\perp dr$, then $W=0$
Clearly, the moments when displacement vector makes $90^{\circ }$ angle with acceleration, work done will be zero.