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The circular motion of a particle with constant speed is -
A
Periodic and simple harmonic
B
Simple harmonic but not periodic
C
Neither periodic nor simple harmonic
D
Periodic but not simple harmonic
Detailed Solution
A periodic motion repeats itself after equal intervals of time. A particle moving in a circle with constant speed returns to the same point after every time period $T = \dfrac{2\pi r}{v}$, so the motion is periodic.
Simple harmonic motion is a to and fro motion along a straight line about a mean position, under a restoring force proportional to the displacement ($F = -kx$).
Uniform circular motion is not a to and fro motion along a line, and the centripetal force is not of the form $-kx$ along the path, so it is not simple harmonic.
However, the projection of uniform circular motion on any diameter executes SHM.
So the circular motion with constant speed is periodic but not simple harmonic.
Simple harmonic motion is a to and fro motion along a straight line about a mean position, under a restoring force proportional to the displacement ($F = -kx$).
Uniform circular motion is not a to and fro motion along a line, and the centripetal force is not of the form $-kx$ along the path, so it is not simple harmonic.
However, the projection of uniform circular motion on any diameter executes SHM.
So the circular motion with constant speed is periodic but not simple harmonic.