Question

Assertion: A planet moves faster, when it is closer to the sun in its orbit and vice versa
Reason: Orbital velocity for an orbiting planet is constant.
A. Both assertion and reason are correct and reason is the correct explanation for assertion.
B. Both assertion and reason are correct but reason is not the correct explanation for assertion.
C. Assertion is correct but reason is incorrect
D. Assertion is incorrect but reason is correct

Answer 1

Hint: Use the law of conservation of angular momentum when the net torque on the system is zero. Use the formula for the angular momentum of the planet when it is moving with velocity v at distance r from the sun and find the relation between v and r.

Complete answer:
When the planet orbits around the sun, the sun exerts a gravitational force of attraction on the planet and the planet exerts a gravitational force of attraction on the sun of equal magnitude but opposite in direction. As a result, the net force on the system is zero. Therefore, the net torque on the system about the position of the sun is zero. When net torque on a system is zero, the angular momentum of the system remains constant.

This means that the angular momentum about the sun is constant. The angular momentum of the planet when it is moving with velocity v at distance r from the sun is given as $L=mvr$.
Since L is constant, mvr is constant. Then this means that $vr=k$, where k is a constant.
Therefore, when the planet moves closer to the sun, the value of r reduces. As a result, the value of v increases so that ‘vr’ remains constant. Hence, the planet moves faster. And when the planet moves away from the sun, the value of r increases. As a result, the planet slows down. Therefore, the given assertion is correct. However, the given reason is incorrect as we just now understand that the orbital speed of the planet changes.

Hence, the correct option is C.

Note:We can also answer the question with the help of law of conservation of mechanical energy in case of gravitational force.Mechanical energy is the sum of potential energy and the kinetic energy of the planet. This means that the sum of the kinetic energy and the potential energy is constant. When the planet comes closer to the sun, its potential energy decreases due to which the kinetic energy of the planet increases and vice versa. As a result, it moves faster when closer to the sun and moves slower when away from the sun.