Chapter 13, Problem 1OQ

To determine

The number of terms in the expression for the total gravitational potential energy.

Answer to Problem 1OQ

Option (c) 10.

Explanation of Solution

Write the expression for the total potential energy.

  $U=U_{12}+U_{13}+U_{14}+U_{15}+U_{23}+U_{24}+U_{25}+U_{34}+U_{35}+U_{45}$

Here, $U$ is the total potential energy of the system, $U_{12}$ is the potential energy between first and second particle, $U_{13}$ is the potential energy between first and third particle, $U_{14}$ is the potential energy between first and fourth particle, $U_{15}$ is the potential energy between the first and fifth particle, $U_{23}$ is the potential energy between second and third particle, $U_{24}$ is the potential energy between second and fourth particle, $U_{25}$ is the potential energy between second and fifth particle, $U_{34}$ is the potential energy between third and fourth particle, $U_{35}$ is the potential energy between third and fifth particle and $U_{45}$ is the potential energy between fourth and fifth particle.

Conclusion:

Therefore, the above expression consists of 10 terms. Thus, option (c) is correct.