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In a solar system, the time-period of revolution of a planet tracing a circular orbit of radius R is proportional to:
APPLY COMPETENCY 4 Marks
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50%
Calculation / Logic
50%
Target Level
MEDIUM
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Q: In a solar system, the time-period of revolution of a planet tracing a circular orbit of radius R is proportional to:

Question Analysis & Solution

Detailed Solution

Step 1: Identify the relevant physical law

According to Kepler's Third Law of Planetary Motion, the square of the time period of revolution ($T$) of a planet around the Sun is directly proportional to the cube of the semi-major axis ($R$) of its orbit.

Step 2: Formulate the mathematical relationship

The relationship is expressed as: $$T^2 \propto R^3$$

Step 3: Solve for T

To find the proportionality for the time period ($T$), we take the square root of both sides: $$T \propto (R^3)^{1/2}$$ $$T \propto R^{3/2}$$

Final Answer: R^{3/2}

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