Question

Potential energy of a particle is given by U = x²- 5x. Which of the following is equilibrium position of the particle?

(1) x = 0

(2) x = 5

(3) x = 2.5

(4) x = 7.5

Answer with explanation please!!

Answer 1

1. x=2.5
As we know that a particle is said to be in equilibrium if net force acting on the particle is zero .
we can also go through tbis formula
Fx= du/dx
For Force=0 we have to make dU/dX = 0.
now put the value in first derivative i.e 2X-5=0 .
x=2.5 ans
Hope this is the answer of your question :)

Answer 2

Answer:

The equilibrium position is x = 2.5

Explanation:

Given, potential energy of a particle is     $U = x^2 - 5x$

Now,the Force acting on a particle is  

                                                        $F = - \frac{dU}{dx}$

                                                  →   $F = - \frac{dU}{dx} = \frac{d}{dx} (x^2 - 5x)$

                                                                        =( 2x - 5 )      

In equilibrium,the resultant Force will be zero.

                           ∴ F = 0

                           → 2x -5 = 0

                           →    $x = \frac{5}{2}$  = 2.5      [Equilibrium position]