Question

Two equal negative charges $-q$ each are fixed at points $(0,-a)$ and $(0,a)$ on y-axis. A positive charge $Q$ is released from rest at the point $(2a,0)$ on the $x$ - axis. The charge $Q$ will

• A. execute simple harmonic motion about the origin
• B. move to the origin and remain at rest
• C. move to infinity
• D. execute oscillatory but not simple harmonic motion

Answer 1

The correct option is D execute oscillatory but not simple harmonic motion

At the position shown particle has acceleration along negative $x$-axis accelerates until it reaches origin.
As the particle crosses origin net force is along positive $x$ axis hence decelerates till its speed becomes zero and reverses direction of motion.
Hence particle oscilaates about origin.


Motion is simple harmonic only if $Q$ is released from a point not very far from the origin on $x$ - axis. Otherwise motion is periodic but not simple harmonic.