Question

Potential energy of a particle at position x is given by U = x2 - 10x + 4. Equilibrium position of the particle will be at ​

Answer 1

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Answer 2

Dear student,

It is given that the potential energy of a particle U(x) = ax - bx². We have to find the equilibrium position of the particles implying that we have to position of x where a and b are constants.

By the formula of potential energy, we know that for conservative forces, we have:

                   Fc.f. = - ( du/ dx)

Putting the given values in the formula, we get:

         Fc.f. = - [d(x² - 10x + 4)/dx]

           0 = - [dx²/dx - 10dx/dx + 0]

           0 = - [2x - 10]

           0 = 10 - 2x

         2x = 10

           x = 5

Hence, the Equilibrium position of the particle will be at 5.