Work Power and Energy 5 Question 6

8. 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 constants. For x0, the functional form of the potential energy U(x) of the particle is

(a)

(b)

(c)

(d)

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Answer:

Correct Answer: 8. (d)

Solution:

  1. F=dUdx

dU=Fdx

or U(x)=0x(kx+ax3)dx

U(x)=kx22ax44

U(x)=0 at x=0 and x=2kaU(x)= negative for x>2ka

From the given function, we can see that F=0 at x=0 i.e. slope of Ux graph is zero at x=0.



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