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Which quantity remains conserved in the motion of planet?

(a) Kinetic energy

(b) Potential energy

(c) Linear momentum

(d) Angular momentum

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Correct option is (d) Angular momentum

In an elliptical orbit, the distance between the Sun and the planet changes with time. So the gravitational potential energy (depends on r) changes, hence the kinetic energy. Since the kinetic energy changes, linear speed is also not constant.

Rate of change in angular momentum of a particle about a centre is:

\(\frac{dL}{dt}\) = r × F

In this case F is the gravitational force of attraction, which acts along the radius r.

So the cross product of r and F is zero.

⇒ Angular momentum is constant.

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