Q. In the figure below, the variation of potential energy of a particle of mass is represented w.r.t its -coordinate. The particle moves under the effect of the conservative force along the -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 -axis.

B

If it is released at , where , then its maximum speed will be and it will perform oscillatory motion.

C

If initially and , then it will cross .

D

and are unstable equilibrium positions of the particle.

Solution:

If the particle is released at the origin, it will try to go in the direction of force.
Here is positive and hence force is negative; as a result, it will move towards negative -axis.
When the particle is released at , it will reach the point of least possible potential energy where it will have maximum kinetic energy.

The particle will now perform oscillatory motion with as mean position.
In (c),
At

So the particle crosses .

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