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AIIMS 2017
Exam
AIIMS
Year
2017
Subject
Physics
Chapter
Gravitation

AIIMS 2017 · Physics · Gravitation

Assertion : Kepler's second law can be understood by conservation...

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(d A / d t)=\left(r^2 \omega\right) / 2.

Options

  1. AIf both assertion and reason are true and reason is the correct explanation of assertion.
  2. BIf both assertion and reason are true but reason is not the correct explanation of assertion.
  3. CIf assertion is true but reason is false.
  4. DIf both assertion and reason are false.

Correct answer

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

Step-by-step solution

According to Kepler's law, dAdt=\frac{d A}{d t}= constant As, dAdt=12r2dθdt=12r2ω\frac{d A}{d t}=\frac{1}{2} r^2 \frac{d \theta}{d t}=\frac{1}{2} r^2 \omega∴mr2ω2m=L2m= constant ∴L= constant \begin{aligned} & \therefore \frac{m r^2 \omega}{2 m}=\frac{L}{2 m}=\text{ constant } \\ & \therefore L=\text{ constant }\end{aligned}$$
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