Question

Four particles, each of mass m, are kept at the four corners of a square of side 'a'. The amount of work done to separate these particles with no interaction between them will be:

(a) 0
(b) 2Gm²​/a
(c) 3Gm²​/a
(d) 4Gm²/a​

Answer 1

The work done to separate four particles at the corners of a square with side 'a' with no interaction between them is zero because there is no change in gravitational potential energy if the particles do not interact.

option a is the correct

Step-by-step explanation:

The question at hand involves calculating the work done to separate four particles of mass m placed at the corners of a square with side a. When dealing with gravitational forces, the work done to move a mass from one point to another is essentially the change in gravitational potential energy.

Since the question specifies that there is no interaction between the particles as they are separated, the gravitational potential energy between any two particles is essentially freed as they are moved infinitely far apart.

When particles are placed at the corners of a square, each particle will experience a gravitational attraction with three other particles with which it shares an edge or a diagonal. Therefore, there are a total of six unique interactions (each edge counts once and each diagonal once). By calculating the work done to separate each pair and summing them up, we can find the total work done. However, since it's given that there is no interaction, the amount of work done is zero.