In planetary motion the areal velocity of position vector of a planet depends on angular velocity - and the distance r of the planet from sun- If so- the correct relation for areal velocity is-

The correct option is B dA dt ∝ w r^ 2 dAdt=L^2T^ 1α w^αr^b L^2T^ 1∝ (T^ 1)^2(L)^b ⇒α =1,b=2 ⇒dAdt #160; ∝ #160;w r^2 ...

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Standard XII

Physics

Dimensional Analysis

In planetary ...

Question

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

\frac{d A}{d t} \propto w r

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\frac{d A}{d t} \propto w^{2} r

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\frac{d A}{d t} \propto w r^{2}

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\frac{d A}{d t} \propto \sqrt{w r}

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Solution

The correct option is B $\frac{d A}{d t} \propto w r^{2}$
$\frac{d A}{d t} = L^{2} T^{- 1} α w^{α} r^{b}$
$L^{2} T^{- 1} \propto (T^{- 1})^{2} (L)^{b}$
$\Rightarrow α = 1, b = 2$
$\Rightarrow \frac{d A}{d t} \propto w r^{2}$

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

The correct option is B dAdt∝wr2dAdt=L2T−1αwαrbL2T−1∝(T−1)2(L)b⇒α=1,b=2⇒dAdt∝wr2

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

The correct option is B $\frac{d A}{d t} \propto w r^{2}$
$\frac{d A}{d t} = L^{2} T^{- 1} α w^{α} r^{b}$
$L^{2} T^{- 1} \propto (T^{- 1})^{2} (L)^{b}$
$\Rightarrow α = 1, b = 2$
$\Rightarrow \frac{d A}{d t} \propto w r^{2}$