Question

four particles each of mass 1kg are at four corners of a square of side 1m. the work done to remove one of the particles to infinity is ​

Answer 1

The work done to remove one of the particles to infinity is (2$\sqrt{2}$+1/$\sqrt{2}$ ) G

Given -

• Mass of particle = 1 kg
• Side of the square = 1 m

System of 4 particles is shown in the attached figure.

Let us calculate the gravitational potential energy in both the cases-

Case 1- (For system of four particles)

Ui = -4 [G m²/a] + [-2 Gm²/$\sqrt{2}$a] where Ui is the initial gravitational potential energy.

Case 2 -(For system of three particles)

Uf = -2 [Gm²/a] + [-Gm²/$\sqrt{2}$a] where uf is the final gravitational potential energy.

We know that work done = Uf - Ui

By substituting the values we get

W = (2$\sqrt{2}$+1/$\sqrt{2}$ ) G