Physics

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


ANSWER

$$\dfrac { dA }{ dt } \propto { w }r^{ 2 }$$


SOLUTION

$$\dfrac{dA}{dt}=L^{2}T^{-1}\alpha w^{\alpha }r^{b}$$

$$L^{2}T^{-1} \propto (T^{-1})^{2}(L)^{b}$$
$$\Rightarrow \alpha =1,b=2 $$
$$\Rightarrow\dfrac{dA}{dt}  \propto  w r^{2} $$
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Single Correct Medium Published on 18th 08, 2020
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