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# A satellite of mass m moves along an elliptical path around the earth. The areal velocity of satellite is proportional to

$(a)\;m \quad (b)\;m^{0} \quad (c)\;m^{-1} \quad (d)\;m^{\frac{1}{2}}$

The areal velocity $\large\frac{dA}{dt}$ =constant
$\large\frac{dA}{dt}=\frac{L}{2 m}$
$L=mvr \sin \theta$ (angular momentum)
$\large\frac{dA}{dt}=\frac{mvr \sin \theta}{2m}$
$\qquad= v r \sin \theta$
$\therefore \large\frac{dA}{dt}$$\; \alpha\; m^0$
Hence b is the correct answer.

edited Feb 17, 2014 by meena.p