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

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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:

Gravitation

Solution:

$L = mvr \Rightarrow L = m \sqrt{\frac{ GM }{ r }} r $
$L = m \sqrt{ GMr } ...$ (i)
$L = 2m \frac{dA}{dt} .... $ (ii)
From (i) & (ii)
$\frac{dA}{dt} \propto \sqrt{r} $
$(dA/dt)_1/(dA/dt)_2 = \sqrt{\frac{4}{1}} = \frac{2}{1}$