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

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 (A) (dA/dt) propto ω r (B) (dA/dt) propto ω2 r (C) (dA/dt) propto ω r2 (D) (dA/dt) propto √ω r

Tardigrade Admin · Accepted Answer

(dA/dt) = (L/2m) = (dA/dt) propto vr propto ω r2

Q. 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

$\frac{d A}{d t} \propto ω r$

$\frac{d A}{d t} \propto ω^{2} r$

$\frac{d A}{d t} \propto ω r^{2}$

$\frac{d A}{d t} \propto ω r$

$\frac{d A}{d t} = \frac{L}{2 m} = \frac{d A}{d t} \propto v r \propto ω r^{2}$

Q. 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

dtdA​∝ωr

dtdA​∝ω2r

dtdA​∝ωr2

dtdA​∝ωr​

dtdA​=2mL​=dtdA​∝vr∝ωr2

Q. 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

$\frac{d A}{d t} \propto ω r$

$\frac{d A}{d t} \propto ω^{2} r$

$\frac{d A}{d t} \propto ω r^{2}$

$\frac{d A}{d t} \propto ω r$

$\frac{d A}{d t} = \frac{L}{2 m} = \frac{d A}{d t} \propto v r \propto ω r^{2}$