Q.

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

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a

Move to infinity

b

Move to the origin and remain at rest

c

Execute simple harmonic motion about the origin

d

Execute oscillatory but not simple harmonic motion

answer is D.

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Detailed Solution

(d)By symmetry of problem the components of force on Q due to charges at A and B along y-axis will cancel each other while along x-axis will add up and will be along CO. Under the action of this force charge Q will move towards O. If at any time charge Q is at a distance x from O. Net force on charge Q
 

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As the restoring force Fnet is not linear, motion will be oscillatory (with amplitude 2a) but not simple harmonic.

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