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 (dA/dt)=(r2ω)/2.

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 (dA/dt)=(r2ω)/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

Tardigrade Admin · Accepted Answer

According to Keplerâs law, (dA/dt) = constant As, (dA/dt)=(1/2)r2 (dθ/dt)=(1/2)r2ω ∴ (mr2ω/2m)=(L/2m) = constant ∴ L = constant

Q. 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 $(d A / d t) = (r^{2} ω) /2.$

If both assertion and reason are true and reason is the correct explanation of assertion

If both assertion and reason are true but reason is not the correct explanation of assertion

If assertion is true but reason is false

If both assertion and reason are false

According to Kepler’s law, $\frac{d A}{d t}$ = constant
As, $\frac{d A}{d t} = \frac{1}{2} r^{2} \frac{d θ}{d t} = \frac{1}{2} r^{2} ω$
$∴ \frac{m r ^{2} ω}{2 m} = \frac{L}{2 m}$ = constant
$∴$ L = constant

Q. 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 (dA/dt)=(r2ω)/2.