Determine whether the statement is true or false.

For an isolated system of particles, the total gravitational potential energy follows the superposition principle.

 

The given statement is true.

• Gravitational potential energy is the energy possessed or acquired by an object due to a change in its position when it is present in a gravitational field.

$\mathrm{U}= -\frac{{\mathrm{Gm}}_1{\mathrm{m}}_2}{\mathrm{r}}$

where U= gravitational potential energy,

m1 and m2 are the masses of particles.

• The principle of superposition states that "The resultant gravitational force F acting on a particle due to the number of point masses is equal to the vector sum of forces exerted by the individual masses on the given particle".

Since gravitational potential energy arises due to the interaction between two masses, the total potential energy of an isolated system equals the sum of energies for all possible pairs of constituent particles. Hence, it follows the superposition principle.