a system consists of four particles how many terms appear in the expression for the total gravitational potential energy of the system
Six terms . One for when the second particle is brought in.
Two for then the third particle is brought in. Three for when the third particle is brought in.
You could also think of it as 12 QiQj/Rij pairs, but they occur in six equal pairs, and must not be double-counted.
This answer is correct. However, there is a back-story. Each of the four exerts a gravitational force on the others. As the distance between them approaches infinity, that value of that force approaches zero. Initially, one particle points to the other three. Three terms. Remove one as it approaches infinite distance. You are left with one pointing to two. Add two. Finally, you have one pointing to the other. Add one. Total is six terms.
The number of terms that appear in the expression for the total gravitational potential energy of a system with four particles can be calculated using the formula for combinations.
In this case, we want to find the number of combinations of 4 objects taken 2 at a time (since gravitational potential energy depends on pairs of particles).
The formula for combinations is given by: C(n, k) = n! / (k!(n-k)!)
Plugging in the values, we have:
n = 4 (number of particles)
k = 2 (number of particles taken at a time)
C(4, 2) = 4! / (2!(4-2)!)
= 4! / (2!2!)
= (4 x 3 x 2 x 1) / ((2 x 1)(2 x 1))
= 24 / (4)
= 6
Therefore, there are 6 terms that appear in the expression for the total gravitational potential energy of the system.
To find the number of terms in the expression for the total gravitational potential energy of a system consisting of four particles, we need to understand how the gravitational potential energy is calculated.
The gravitational potential energy between two particles can be given by the equation:
PE = -(G * m1 * m2) / r
where G is the gravitational constant, m1 and m2 are the masses of the two particles, and r is the distance between them.
For a system of four particles, we need to calculate the gravitational potential energy between each pair of particles. Let's label the particles as 1, 2, 3, and 4.
So, we need to calculate the gravitational potential energy for particles (1, 2), (1, 3), (1, 4), (2, 3), (2, 4), and (3, 4).
This gives us a total of 6 terms in the expression for the total gravitational potential energy. Each pair of particles contributes one term.
Therefore, in a system consisting of four particles, the expression for the total gravitational potential energy will have 6 terms.