The potential energy of a particle of mass 0.1 kg , moving along the X-axis , is given by `U=5x(x-4) J`, where x is in metres. Choose the wrong option.

Options

A. The particle is acted upon by a variable force.
B. The minimum potential energy during motion is `-20 J`.
C. The speed of the particle is maximum at `x = 2m`.
D. `x = 2` is position of ustable equilibrium

Answer

A, B, C

Explanation

`U = 5x^(2) - 20x`
`F = -(dU)/(dx) -[10x - 20]`
`:. X = 2` is position of equilibrium
Now `(d^(2)U)/(dx^(2)) = 10 gt 0`
`:.` Only one minima
`rArr x = 2` is minima `rArr KE` is maximum at `x = 2`
`U(x = 2) = -20 J`