The force acting on a particle of mass m moving along the x-axis is given by F(x) = Ax^ - Bx. Which one of the following is the potential energy of the particle ?

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Q: 20 (NDA-II/2017)
The force acting on a particle of mass m moving along the x-axis is given by F(x) = Ax^ - Bx.
Which one of the following is the potential energy of the particle ?

question_subject: 

Science

question_exam: 

NDA-II

stats: 

0,3,2,0,3,0,2

keywords: 

{'potential energy': [0, 0, 1, 4], 'particle': [0, 2, 8, 30], 'force': [0, 0, 0, 2], 'bx': [0, 0, 0, 1], 'mass': [0, 0, 2, 3], '3b': [0, 0, 0, 1], '2ax': [0, 0, 0, 1]}

The force acting on a particle is related to the potential energy through the equation F(x) = -dU(x)/dx, where U(x) is the potential energy. In this question, the force is given as F(x) = Ax^2 - Bx.

To find the potential energy, we can integrate the force with respect to x.

Integrating F(x) = Ax^2 - Bx with respect to x, we get U(x) = (A/3)x^3 - (B/2)x^2 + C, where C is the constant of integration.

However, since potential energy is defined up to a constant, we can set C = 0.

Therefore, the potential energy of the particle is U(x) = (A/3)x^3 - (B/2)x^2.

Looking at the options:

Option 1: 2Ax - B. This is not the correct potential energy, as it is a linear function of x, while the potential energy should be a cubic function of x.

Option 2: -(2Ax - 3B)/6. This is the correct potential energy, which matches the result we obtained by integrating the force.

Option