The radii of circular orbits of two satellite `A` and `B` of the earth are `4R` and `R`, respectively. If the speed of satellite `A` is `3v`, then the speed of satellite `B` will be

Options

A. `(3V)/(4)`
B. `6V`
C. `12V`
D. `(3V)/(2)`

Answer

B

Explanation

Orbital speed of the satellite around the earth is
` v = sqrt((GM)/( r))`
where, G = universal gravitational constant, M=mass of earth , r=radius of the orbit of the satellite For satellite A
`r_A = 4R, v_A = 3V, v_A = sqrt((GM)/(r_A))` ....(i)
For satellite B
` r_B = R, v_B = ? , v_B = sqrt((GM)/(r_B))` ...(ii) Dividing equation (ii) by equation (i), we get
`v_B/v_A =sqrt(r_A/r_B) " or " v_B = v_A sqrt(r_A/r_B)`
Substituting the given values, we get
` v_B = 3V sqrt((4R)/( R)) = 6V`