Question

19. A satellite goes along an elliptical path around earth. The rate of change of area swept by the line joining earth and the satellite is proportional to (a) r/2 (c)r3/2 (d) r2

Answer 1

Answer:

$r^\frac{1}{2}$

Explanation:

Angular momentum, L = m v r

areal velocity = $\frac{dA}{dt}$

according to kepler's 2nd law

$\frac{dA}{dt}=\frac{L}{2m}$

since, we know that

$v=\sqrt{\frac{Gm}{r} }$

areal velocity= $\frac{mvr}{2m} = \frac{vr}{2}$

now substituting value of v in areal velocity we get

$\frac{1}{2}\sqrt{GMr}$

hence from above equation of rate of change of area swept i.e. areal velocity is proportional to   $r^\frac{1}{2}$