In planetary motion the areal velocity of position vector of a planet depends on angular velocity (m) and the distance of the planet from sup (r). If so the correct relation for areal velocity is

Options

A. `dA/dt alpha omega r`
B. `dA/dt alpha omega^(2) r`
C. `dA/dt alpha omega r^(2)`
D. `dA/dt alpha sqrt(omega r)`

Answer

C

Explanation

The relation for areal velocity is,
`dA/dt alpha omega^(a)r^(b)`
`dA/dt = k omega^(a)r^(b)`
From principal of homogenity of dimensions.
`[L^(2)T^(-1)] = [T^(-1)]^(a)[L]^(b)`
` L^(2) = L^(b) implies b = 2`
` T^(-1) = T^(-a) implies a = 1`
`implies dA/dt alpha omega r^(2)