Satellites A and B are orbiting around the earth in orbits of ratio R and 4R respectively. The ratio of their areal velocities is:

Question

Satellites A and B are orbiting around the earth in orbits of ratio R and 4R respectively. The ratio of their areal velocities is: (A) 1: 2 (B) 1: 4 (C) 1: 8 (D) 1: 16

Tardigrade Admin · Accepted Answer

L = mvr ⇒ L = m √( GM / r ) r L = m √ GMr ... (i) L = 2m (dA/dt) .... (ii) From (i) (ii) (dA/dt) propto √r (dA/dt)1/(dA/dt)2 = √(4/1) = (2/1)

Q. Satellites $A$ and $B$ are orbiting around the earth in orbits of ratio $R$ and $4 R$ respectively. The ratio of their areal velocities is:

1 : 2

1 : 4

1 : 8

1 : 16

$L = m v r \Rightarrow L = m \frac{GM}{r} r$
$L = m GM r ...$ (i)
$L = 2 m \frac{d A}{d t} ....$ (ii)
From (i) & (ii)
$\frac{d A}{d t} \propto r$
$(d A / d t)_{1} / (d A / d t)_{2} = \frac{4}{1} = \frac{2}{1}$

Q. Satellites A and B are orbiting around the earth in orbits of ratio R and 4R respectively. The ratio of their areal velocities is: