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. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Both Assertion and Reason are incorrect

Answer 1

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

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