Two identical satellites are orbiting are orbiting at distances R and 7R from the surface of the earth, R being the radius of the earth. The ratio of their

Options

A. total energies is `4` and potential and kinetic energies is `2`
B. potential energies is `4`
C. kinetic energies is `4`
D. total energies is `4`

Answer

B, C, D

Explanation

Distance of the two satellites from the centre of the earth are `r_(1) =2R` and `r_(2)=8R`, respectively (`R=` earth's radius). Their potential energies are
`V_(1)=-(GmM)/(r_(1))` and `V_(2)=-(GmM)/(r_(2))`
Their ratio is `(V_(1))/(V_(2))=(r_(2))/(r_(1))=(8R)/(2R)=4`
The kinetic energy of a satellite can be obtained from the relation.
`(mv^(2))/r=(GmM)/(r^(2))`
or `K=1/2mv^(2)=(GmM)/(2r)`
`K_(1)=(GmM)/(2r_(1))` and `K_(2)=(GmM)/(2r_(2))`
The ratio of their kinetic energies is
`(K_(1))/(K_(2))=(r_(2))/(r_(1))=(8R)/(2R)=4`
Their total energies are
`E_(1)=(GmM)/(r_(1))+(GmM)/(2r_(1))=-(GmM)/(2r_(1))`
and `E_(2)=-(GmM)/(r_(2))+(GmM)/(2r_(2))=-(GmM)/(2r_(2))`
Their ratio is `(E_(1))/(E_(2))=(r_(2))/(r_(1))=(8R)/(2R)=4`
Hence,the correct choices are b, c and d.