Question

According to Kepler's second law of planetary motion, the magnitude of areal velocity \(\left(\frac{\Delta A}{\Delta t}\right)\) of a planet of mass '\(m\)' revolving around the sun is constant and is equal to ('\(p\)' is the linear momentum and '\(L\)' is the angular momentum)

• A. \(\frac{p^{2}}{2m}\)
• B. \(2mL\)
• C. \(\frac{p}{m}\)
• D. \(\frac{L}{2m}\)

Hint:

The area swept per unit time equals half of the angular momentum divided by the mass.

Answer 1

The Correct Option is D

Step 1: Link with conservation
Kepler's second law is the statement that angular momentum is conserved for the planet.

Step 2: Eliminate options
$\dfrac{p^{2}}{2m}$ is kinetic energy and $\dfrac{p}{m}$ is speed, neither is an area rate. $2mL$ has the wrong dimensions.

Step 3: Correct form
Only $\dfrac{L}{2m}$ has the dimension of area per unit time.

Final Answer:
Areal velocity is L over 2m. \[ \boxed{\text{(D) }\dfrac{L}{2m}} \]