Two identical satellite are at `R` and `7R` away from earth surface, the wrong statement is (`R`=radius of earth)

Options

A. The ratio of their total energies will be 4 but the ratio of their potential and kinetic energies will be 2
B. The ratio of their potential energies will be 4
C. The ratio of their kinetic energies will be 4
D. The ratio of their total energies will be 4

Answer

A

Explanation

For a revolving satellite, with an orbital radius r,
`P.E.(U)=-(GMm)/(r ), K.E. = (GMm)/(2r)`
and total energy `E=U+K=-(GMm)/(2r)`
For the two satellites,
`r_(1)=R+R=2R` and `r_(2)=R+7R=8R`
`therefore (U_(1))/(U_(2))=(r_(2))/(r_(1))=4, (K_(1))/(K_(2))=(8R)/(2R)=4`
and `(E_(1))/(E_(2))=(8R)/(2R)=4`
Thus (b), (c ) and (d) are correct and (a) is wrong.