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A particle is acted simultaneously by mu...

A particle is acted simultaneously by mutually perpendicular simple harmonic motions x=a cos`omegat` and `y=asinomegat`. The trajectory of motion of the particle will be

A

an ellipse

B

a parabola

C

a circle

D

a straight line.

Text Solution

Verified by Experts

The correct Answer is:
C
Given
`x=acosomegat` . . . (i)
`y=asinomegat`
Squaring and adding (i) and (ii), we get
`x^(2)+y^(2)=a^(2)cos^(2)omegat+a^(2)sin^(2)omegat=a^(2)`
It is an equation of circle. Thus, trajectory of motion will be circle.
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