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:

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

##### 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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