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).
Create a free account to view solution
View Solution FreeMore Work, Power and Energy Questions
A 50 gm bullet moving with a velocity of 10 m/s gets embedded into a 950 gm stationary body. The loss in kinetic energy ...The quantities that are conserved in elastic collision are :-...An α particle is taken from points A to B having potentials 40 V and 20 V repectively then work done by electrostat...Radiation coming from transitions n = 2 to n = 1 of hydrogen atom falls on helium ions in n = 1 and n = 2 states. Which ...A solid sphere of radius R and density ρ is attached to one end of a mass-less spring of force constant k. The othe...