Two satellite A and B, ratio of masses `3:1` are in circular orbits of radii `r and 4r`. Then ratio mechanical energy of A and B is

Options

A. `1:3`
B. `3:1`
C. `3:4`
D. `12:1`

Answer

D

Explanation

Energy of satellite is given by
`E=-(GMm)/(2r)or E prop (m)/(r)`
`rArr (E_(A))/(E_(B))=(m_(A))/(m_(B))xx(r_(B))/(r_(A))=(3)/(1)xx(4r)/(r)" "{because (m_(A))/(m_(B))=(3)/(1),(r_(B))/(r_(A))=(4r)/(r)}`
`rArr (E_(A))/(E_(B))=(12)/(1)`.