The potential energy of a particle of mass 0. | vedclass

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(B, C) Given $V = A x(x-4) = A x^2 - 4Ax \ J$.The force acting on the particle is $F = -\frac{dV}{dx} = -(2Ax - 4A) = -2A(x-2) \ N$.Since $F \propto -

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The speed of the particle is maximum at $x = 2 \ m$

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(B, C) Given $V = A x(x-4) = A x^2 - 4Ax \ J$.The force acting on the particle is $F = -\frac{dV}{dx} = -(2Ax - 4A) = -2A(x-2) \ N$.Since $F \propto -(x-2)$, the particle executes Simple Harmonic Motion $(SHM)$ about the mean position $x = 2 \ m$.In $SHM$, the speed is maximum at the mean position, so the speed is maximum at $x = 2 \ m$.Comparing $F = -2A(x-2)$ with the standard $SHM$ equation $F = -k(x-x_0)$, we get the spring constant $k = 2A$.The angular frequency is $\omega = \sqrt{\frac{k}{m}} = \sqrt{\frac{2A}{0.02}} = \sqrt{100A} = 10\sqrt{A} \ rad/s$.The time period is $T = \frac{2\pi}{\omega} = \frac{2\pi}{10\sqrt{A}} = \frac{\pi}{5\sqrt{A}} \ s$.Thus, statements $B$ and $C$ are correct.

The potential energy of a particle of mass $0.02 \ kg$ moving along the $x$-axis is given by $V = A x(x-4) \ J$, where $x$ is in metres and $A$ is a constant. Which of the following is/are correct statement$(s)$?

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