Work, Power and EnergyHard
Question
A particle, which is constrained to move along x-axis, is subjected to a force in the same direction which varies with the distance x of the particle from the origin as F(x) = - kx + ax3. Here, k and a are positive constant. For x ≥ 0, the functional from of the potental energy U(x) of the particle is
Options
A.
B.
C.
D.
Solution
F = - 
∴ dU = -F.dx
or U(x) = -
(-kx + ax3).dx
U(x) =
U(x) = 0 at x = 0 and x =
U(x) = negative for x >
From the given function we can see that
F = 0 at x = 0 i.e., slope U-x graph is zero at x = 0
Therefore, the most appropriate option is (d).
∴ dU = -F.dx
or U(x) = -
(-kx + ax3).dx U(x) =
U(x) = 0 at x = 0 and x =
U(x) = negative for x >
From the given function we can see that
F = 0 at x = 0 i.e., slope U-x graph is zero at x = 0
Therefore, the most appropriate option is (d).
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