A satellite is moving around the earth's with speed `v` in a circular orbit of radius `r`. If the orbit radius is decreases by `1%` , its speed will

Options

A. increase by `1%`
B. increases by `0.5%`
C. decrease by `1%`
D. decreases by `0.5%`

Answer

B

Explanation

Orbital speed of satellite, `upsilon = sqrt((GM)/(r ))` …(i)
If `r` decreases, `upsilon` increases differentiating (i) we get
`d upsilon = - (1)/(2) sqrt(GM) r^(-3//2) dr = - (sqrt(GM))/(2r^(3//2)) dr`
`:. (d upsilon)/(upsilon) = (1)/(2) (sqrt(GM))/(r^(3//2)) dr//sqrt((GM//r)) = -(1)/(2) (dr)/(r )`
`:.%` increase in velocity `= (d upsilon)/(upsilon) xx 100`
`= - (1)/(2)(dr)/(r ) xx 100 = - (1)/(2) xx (-(1)/(100)) xx 100 = 0.5%`