Keplers Law: Practice Problem & Solution
Assertion (A): Period of revolution of satellite in circular orbit around earth is inversely proportional to cube of its orbital speed. Reason (R): Period of revolution in uniform circular motion is given by \( T = \frac{2\pi r}{v} \) where \( r \) is radius of orbit and \( v \) is speed.
Short Solution (Best for NEET):
To solve this problem, we apply the core principles of Keplers Law. Understanding the underlying formula is key to arriving at the correct answer below:
Assertion (A) is true. For a satellite in circular orbit, orbital speed \( v = \sqrt{\frac{GM}{r}} \) implying \( r \propto \frac{1}{v^2} \). The period is \( T = \frac{2\pi r}{v} \). Substituting \( r \), we get \( T \propto \frac{1/v^2}{v} \propto \frac{1}{v^3} \).
Reason (R) is true. The formula \( T = \frac{2\pi r}{v} \) is the correct definition for the period of uniform circular motion. However, (R) is a kinematic definition and does not explain the dynamic relationship between \( T \) and \( v \) for a satellite, which requires considering gravity. Thus, (R) is not the correct explanation of (A).
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