Question

In a planetary motion, the areal velocity of position vector of a planet depends on angular velocity ($ω$) and distance ($r$) of the planet from the sun. The correct relation for areal velocity $\fracdAdt$ is

• A. $\fracdAdt \propto ω r$
• B. $\fracdAdt \propto ω r²$
• C. $\fracdAdt \propto \frac\omegar²$
• D. $\fracdAdt \propto \frac\omegar$

Hint:

Kepler's second law: Areal velocity is constant for a planet, $\fracdAdt = \frac12 r² ω$.

Answer 1

The Correct Option is B

Step 1: Areal velocity $\fracdAdt = \frac12 r² ω$ (from $dA = \frac12 r² dθ$, $ω = dθ/dt$).

Step 2: So $\fracdAdt \propto ω r²$.