Question

A cluster consisting of 10 stars has a total gravitational potential energy of $30 \times {10^{10}}$ Joules. What is the potential energy of each star?
A. $30 \times {10^{10}}$Joules
B. $30 \times {10^9}$Joules
C. $30 \times {10^8}$Joules
D. This energy cannot be divided, since it is the energy of the system.

Answer 1

Hint: The gravitational potential energy is the amount of work done when one star is brought from infinity to a particular point in the presence of other stars. So, the cluster of stars acts as a group.

Complete step by step answer:
The energy possessed by a body by virtue of its specific position or changed configuration i.e., shape, size is called potential energy. The potential energy possessed by a body due to its position relative to the centre of earth is called gravitational potential energy. When the distance of the body from the centre of earth is larger, greater is the gravitational potential energy. For example – A stone placed at a certain height has the potential energy stored in it because of its position at that height.
The gravitational potential energy of a system of particles is equal to the work done by some external force when a particle is brought from infinity to its position in the presence of other particles of the system. When the particle is brought in the presence of other particles, this particle experiences some force due to the other particles.
In this cluster I.e., group of 10 stars has a total gravitational potential energy of $30 \times {10^{10}}$ Joules which means the amount of work done by the external force to bring any one star from infinity to a particular point in the presence of other 9 stars. Hence, the potential energy of each star cannot be determined as it is the energy of the whole system.
Therefore, option D is correct.

Note:The gravitational potential energy cannot be divided into small parts of energy of each star as it is the energy of the whole system. The other stars also exert some force on that star which is brought from infinity.