Question

lf 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, and its areal velocity is ______.

Options

• `L/m`

• `(4L)/m`

• `L/(2m)`

• `(2L)/m`

Answer 1

lf 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, and its areal velocity is `underlinebb(L/(2m))`

Explanation:

Areal velocity; `(dA)/(dt)`

dA = `1/2r^2d theta`

⇒ `(dA)/(dt) = 1/2r^2 (d theta)/(dt) = 1/2r^2omega`

Also, L = mvr = mr²ω

∴ `(dA)/(dt) = 1/2 L/m`