Question

For inverse square law forces, the mathematical statement of the virial theorem is (where \( \langle T \rangle \) and \( \langle V \rangle \) are the averages of kinetic and potential energies):

• A. \( 2\langle T \rangle = -V \)
• B. \( 2\langle T \rangle = \langle V \rangle \)
• C. \( \langle T \rangle = \langle V \rangle \)
• D. \( \langle T \rangle = -2\langle V \rangle \)

Hint:

The virial theorem helps in understanding the relationship between kinetic and potential energy in bound systems.

Answer 1

The Correct Option is D

The virial theorem states:
\[ 2 \langle T \rangle + \langle V \rangle = 0 \] For inverse square law forces (e.g., gravitational or Coulomb forces), the relation simplifies to:
\[ \langle T \rangle = -\frac{1}{2} \langle V \rangle \]