Question

the potential energy of a particle at position x is given by u =x square -3x the equlilbrium position of a particle is​

Answer 1

Answer:

• The equilibrium position of the particle is 1.5 units

Explanation:

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Given, the equation of potential energy is given as U = x² - 3 x ,  and we need to find the equilibrium position of the particle. We know that for a particle to be in equilibrium the Force should be zero. i.e. F = 0 or dU/dx = 0. From the formula we know that,

⇒ F = dU/dx

Here,

• F Denotes Force.
• U Denotes Potential energy.
• dx Denotes Small Displacement.

Substituting the values,

⇒ 0 = d(x² - 3 x)/dx

⇒ 0 = 2 x - 3

⇒ 2x = 3

⇒ x = 3/2

⇒ x = 1.5

⇒ x = 1.5 units

∴ The equilibrium position of the particle is 1.5 units.

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