If a graph is plotted between `T^(2)` and `r^(3)` for a planet, then its slope will be be (where `M_(S)` is the mass of the sun)

Options

A. `(4pi)/(GM_(S))`
B. `(GM_(S))/(4pi)`
C. `4piGM_(S)`
D. `GM_(S)`

Answer

A

Explanation

Time period of a revolution of a planet,
`T=(2pir)/r=(2pir)/(sqrt((GM_(S))/r))=(2pir^(3//2))/(sqrt(GM_(S))`
Where `M_(S)` is the mass of the sun. Squaring both sides, we get
`T_(2)=(4pi^(2)r^(3))/(GM_(S))`
The graphs between `T_(2) and r_(3)` is a straight line whose slope is `(4pi^(2))/(GM_(S))`