If r is the distance between the Earth and the Sun. Then, angular momentum of the Earth around the sun is proportional to

Options

A. `sqrt(r)`
B. `r^(3//2)`
C. `r`
D. None of these

Answer

A

Explanation

According to Kepler's third law,
`T^(2) propr^(3)rArr T propr^(3//2)`
We have `omega=(2pi)/(T)rArr omega propr^(-3//2)`
Now, `L=mr^(2)omegarArr L propr^(2) and lpropomega`, i.e,`lpropr^(-3//2)`
`rArr L prop r^(2).r^(-3//2) :. L prop r^(1//2)`.