In planetary motion,the areal velocity of the | vedclass

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(C) The areal velocity $\frac{dA}{dt}$ is defined as the rate at which the area is swept by the position vector of the planet.Given that $\frac{dA}{dt

Vedclass · Accepted Answer

$\frac{dA}{dt} \propto \omega r^2$

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(C) The areal velocity $\frac{dA}{dt}$ is defined as the rate at which the area is swept by the position vector of the planet.Given that $\frac{dA}{dt}$ depends on angular velocity $\omega$ and distance $r$,we can write: $\frac{dA}{dt} = K \omega^a r^b$.The dimensional formula for areal velocity $\frac{dA}{dt}$ is $[L^2 T^{-1}]$.The dimensional formula for angular velocity $\omega$ is $[T^{-1}]$ and for distance $r$ is $[L]$.Substituting these into the equation: $[L^2 T^{-1}] = [T^{-1}]^a [L]^b$.Comparing the exponents of $L$ and $T$ on both sides:For $T$: $-a = -1 \Rightarrow a = 1$.For $L$: $b = 2$.Therefore,the relation is $\frac{dA}{dt} \propto \omega r^2$.

In planetary motion,the areal velocity of the position vector of a planet depends on the angular velocity $\omega$ and the distance of the planet from the sun $r$. The correct relation for areal velocity is:

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