Question

Assertion : Kepler’s second law can be understood by conservation of angular momentum principle.
Reason : Kepler’s second law is related with areal velocity which can further be proved to be based on conservation of angular momentum as $\left(dA/dt\right)=\left(r^{2}\omega\right)/2.$

• A. If both assertion and reason are true and reason is the correct explanation of assertion
• B. If both assertion and reason are true but reason is not the correct explanation of assertion
• C. If assertion is true but reason is false
• D. If both assertion and reason are false

Answer 1

Answer: (A)

According to Kepler’s law, $\frac{dA}{dt}$ = constant
As, $\frac{dA}{dt}=\frac{1}{2}r^{2} \frac{d\theta}{dt}=\frac{1}{2}r^{2}\omega$
$\therefore \, \frac{mr^{2}\omega}{2m}=\frac{L}{2m}$ = constant
$\therefore \,$ L = constant