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Q.

In figure, the variation of potential energy of a particle of mass m = 2 kg is represented w.r.t its x-coordinate. The particle moves under the effect of the conservative force along the x-axis. Which of the following statements is incorrect about the particle?

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a

If it is released at the origin, it will move in negative x-axis.

b

If it is released at x = 2 + Δ, where Δ → 0, then its maximum speed will be 5 ms-1 and it will perform oscillatory motion.

c

If initially x=−10 and u→=6 i^, then it will cross x = 10.

d

x=−5 and x=+5 are unstable equilibrium positions of the particle.

answer is D.

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Detailed Solution

If the particle is released at the origin, it will try to go in the direction of force. Here dU/dx is positive and hence force is negative; as a result, it will move towards negative x-axis.When the particle is released at x = 2 + Δ, it will reach the least possible potential point of energy (-15 J) where it will have maximum kinetic energy12mvmax 2=25vmax =5 ms−1The particle will now perform oscillatory motion with x = 5 as mean position.In (3), Ei=ui+ki=15+6=21 JAt x=10, Uf=20    Kf=1≠0So the particle crosses x = 10.
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