Question

Find the potential energy of a system of four particles placed at the vertices of a square of side l

Answer 1

Answer

Explanation:The P.E of 4 vertices must be substracted from the P.E between the diagonals

Answer 2

Answer:

the potential energy of the system of four particles placed at the vertices of a square of side length "a" is - 2 * G * m^2 * (1 + sqrt(2)) / a.

Explanation:

In order to find the potential energy of a system of four particles placed at the vertices of a square of side length "a", we need to consider the gravitational potential energy between each pair of particles.

Let's assume that each particle has a mass "m" and that the gravitational constant is "G". Then, the potential energy between two particles at a distance "r" is given by:

U = - G * m^2 / r

Since each particle is equidistant from the other three particles, the potential energy between each pair of particles is the same. We can calculate the total potential energy of the system by summing up the potential energy between each pair of particles.

First, let's consider the potential energy between particles placed at adjacent vertices of the square. In this case, the distance between the particles is "a". So, the potential energy between each pair of adjacent particles is:

U_adjacent = - G * m^2 / a

There are two pairs of adjacent particles, so the total potential energy between adjacent particles is:

U_total_adjacent = 2 * U_adjacent = - 2 * G * m^2 / a

Now, let's consider the potential energy between particles placed at opposite vertices of the square. In this case, the distance between the particles is "sqrt(2) * a". So, the potential energy between each pair of opposite particles is:

U_opposite = - G * m^2 / (sqrt(2) * a)

There are two pairs of opposite particles, so the total potential energy between opposite particles is:

U_total_opposite = 2 * U_opposite = - 2 * G * m^2 / (sqrt(2) * a)

Finally, the total potential energy of the system is the sum of the potential energy between adjacent particles and the potential energy between opposite particles:

U_total = U_total_adjacent + U_total_opposite = - 2 * G * m^2 / a - 2 * G * m^2 / (sqrt(2) * a) = - 2 * G * m^2 * (1 + sqrt(2)) / a

Therefore, the potential energy of the system of four particles placed at the vertices of a square of side length "a" is - 2 * G * m^2 * (1 + sqrt(2)) / a.

To learn more about potential energy from the link below

https://brainly.in/question/2769084

To learn more about  gravitational constant  from the link below

https://brainly.in/question/3841670

#SPJ3