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 :

Options

A. `(2L)/(m)`
B. `(4L)/(m)`
C. `(L)/(2m)`
D. `(L)/(m)`

Answer

C

Explanation

Let a planet moving around the sun at a distance r covers an angular displacement `(Delta theta)` in time `Delta t`.
`:. Delta A = (1)/(2) r^(2) Delta theta`
`(Delta A)/(Delta t) = (1)/(2) r^(2) (Delta theta)/(Delta t)`
since `L = m r^(2) omega`
`(Delta A)/(Delta t) = (1)/(2) r^(2) omega = (L)/(2m)`