In planetary motion the areal velocity of position vector of a planet depends on angular velocity - and the distance of the planet from sun r- If so the correct relation for areal velocity is-d A-d t-2 rB- d A-d t- rC- d A-d t- r2D- d A-d t- r

The correct option is C dA/dt=L/2m=mvr/2m=1/2ω r^2 [As angular momentum L=mvr and v=r ω] ∴ dA/dt ∝ ω r^2 ...

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Standard XII

Physics

Kepler's Law

In planetary ...

Question

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

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Solution

The correct option is
C

$\frac{d A}{d t} = \frac{L}{2 m} = c o n s t a n t$
$\frac{d A}{d t} = \frac{m v r}{2 m} = \frac{1}{2} ω r^{2} [A s a n g u l a r m o m e n t u m L = m v r a n d v = r ω] ∴ \frac{d A}{d t} \propto ω r^{2}$

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

The correct option is C dAdt=L2m=constantdAdt=mvr2m=12ωr2 [As angular momentum L=mvr and v=rω]∴ dAdt ∝ ωr2

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

The correct option is
C

$\frac{d A}{d t} = \frac{L}{2 m} = c o n s t a n t$
$\frac{d A}{d t} = \frac{m v r}{2 m} = \frac{1}{2} ω r^{2} [A s a n g u l a r m o m e n t u m L = m v r a n d v = r ω] ∴ \frac{d A}{d t} \propto ω r^{2}$