The angular momentum of a planet of mass M moving around the sun in an elliptical orbit is $\vec{L}$. The magnitude of the areal velocity of the planet is ;

JEE Main · 2021 · 18 Mar 2021 · Shift 2 · Gravitation

The angular momentum of a planet of mass M moving around the sun in an elliptical orbit is

L

. The magnitude of the areal velocity of the planet is ;

(A) $\frac{2 L}{M}$
(B) $\frac{L}{2 M}$ ✓ Correct
(C) $\frac{4 L}{M}$
(D) $\frac{L}{M}$

Answer: (B)

Solution

In a time

d t

the radius vector sweeps a triangle of area

d A = \frac{1}{2} ∣ r \times v d t ∣

, so the areal velocity is

\frac{d A}{d t} = \frac{1}{2} ∣ r \times v ∣

The angular momentum of the planet is

L = M r \times v

, so

∣ r \times v ∣ = \frac{L}{M}

and the areal velocity has magnitude

\frac{L}{2 M}

JEE Main · 2021 · 18 Mar 2021 · Shift 2 · Single correct option

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