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

`r^(1)/(2)`

Step-by-step explanation:

Angular momentum, L = m v r

areal velocity =
`(dA)/(dt)`

according to kepler's 2nd law

`(dA)/(dt)=(L)/(2m)`

since, we know that

`v=\sqrt{(Gm)/(r) }`

areal velocity=
`(mvr)/(2m) = (vr)/(2)`

now substituting value of v in areal velocity we get

`(1)/(2)√(GMr)`

hence from above equation of rate of change of area swept i.e. areal velocity is proportional to
`r^(1)/(2)`