A) \[{{T}^{2}}\propto {{b}^{3}}\]
B) \[{{T}^{2}}\propto {{\left( \frac{a+b}{2} \right)}^{3}}\]
C) \[{{T}^{2}}\propto {{a}^{3}}\]
D) \[{{T}^{2}}\propto {{\left( \frac{a-b}{2} \right)}^{3}}\]
Correct Answer: C
Solution :
From Kepler's third law of planetary motion (also known as law of periods) the square of the period of revolution of any planet around the sun is directly proportional to the cube of the mean distance from the sun. \[{{T}^{2}}\propto {{a}^{3}}\] \[\Rightarrow \] \[{{T}^{2}}=k{{a}^{3}}\] where k is a constant. The larger the distance of planet from the sun, larger will be its period of revolution.
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