Question

If the angular momentum of a planet of mass m, moving around the Sun in a circular orbit is L, about the center of the Sun, its areal velocity is :

• A. $\frac{L}{m}$
• B. $\frac{4L}{m}$
• C. $\frac{L}{2m}$
• D. none of these

Answer 1

The correct option is D none of these

Angular momentum $=L$

Mass of the Planet $=m.$

Relation between Angular momentum, mass of the planet and Areal Velocity of the Planet is given by the formula

$L=2m\times \Delta A/\Delta t$

Proof of this formula,

$L=mvr$

Multiplying and dividing the R.H.S. by 2.

$\therefore L=2mvr/2$

$\therefore L=2m\times v\times r/2$

$\therefore L=2m\times dr/dt\times r/2$

$\therefore L=2m\times dA/dt$

$\therefore L=2m\Delta A/\Delta t$

Hence, Option $D$ is the correct answer.