Question

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

• 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 the kinetic and potential energies respectively and C is the total energy of the system.

Answer 1

Answer: (A)

A shows the kinetic energy, B the total energy and C the potential energy of the system

Answer 2

For a body in circular planetary motion:

1. Kinetic Energy ($KE = \frac{GMm}{2r}$) is always positive and decreases with increasing radius $r$. This corresponds to curve A.
2. Potential Energy ($PE = -\frac{GMm}{r}$) is always negative and becomes less negative (increases) with increasing radius $r$. Its magnitude is twice that of kinetic energy ($|PE| = 2KE$). This corresponds to curve C, which is negative and has a larger magnitude than curve B.
3. Total Energy ($TE = -\frac{GMm}{2r}$) is always negative and becomes less negative (increases) with increasing radius $r$. Its magnitude is equal to kinetic energy ($|TE| = KE$). This corresponds to curve B, which is negative and has a magnitude equal to curve A.

Therefore, A is kinetic energy, B is total energy, and C is potential energy.