The figure shows the variation of energy with the orbit radius of a body in circular planetary motion. Find the correct statements about the curves `A,B` and `C`

Options

A. A shows the kinetic energy, B the total energy and C the potential energy of the system.
B. C shows the total energy, B the kinetic energy and A the potential energy of the system.
C. C and A are kinetic and potential energies respectively and B is the total energy of the system.
D. A and B are kinetic and potential energies respectively and C is the total energy of the system.

Answer

D

Explanation

Total energy = K.E. + P.E. For a bound system, total energy must be negative.
`K.E.=1/2m v^2 ,P.E.=-(GmM)/r`
For a circular orbit , `(mv^2)/r=(GmM)/r^2 rArr 1/2mv^2=1/2(GmM)/r =K.E.`
Total energy = `-(Gm M)/r + (GmM)/(2r) =-(GmM)/(2r)`