Assertion (A): The radius vector from the Sun to a planet sweeps out equal areas in equal intervals of time, so the planet's areal velocity is constant. Reason (R): In a central-force field, angular momentum is conserved. Choose the correct answer.
Options

Question

Assertion (A): The radius vector from the Sun to a planet sweeps out equal areas in equal intervals of time, so the planet's areal velocity is constant. Reason (R): In a central-force field, angular momentum is conserved. Choose the correct answer.

Options

G1 Physics · Accepted Answer

For a central force, torque about the force centre is zero: τ = r×F = 0. Hence angular momentum L is conserved. The areal velocity is dA/dt = L/(2m). Since L is constant, dA/dt is constant. This is Kepler's second law. Thus both A and R are correct, and R explains A. Correct option: A.