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Question

# A particle moves according to the equation x=asinωt,y=acosωt. Then it's resultant motion is

A
uniform circular motion and ω is clockwise.
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B
uniform circular motion and ω is anticlockwise.
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C
nonuniform circular motion with ω clockwise.
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D
nonuniform circular motion with ω anticlockwise.
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Solution

## The correct option is B uniform circular motion and ω is clockwise.Given x=asinωt and y=acosωtso, x2+y2=a2(sin2ωt+cos2ωt)=a2⇒ its a equation of circle. here T=2πω and the angular velocity does not vary with time the particle. So it is uniform motion.now vx=dxdt=aωcosωt and vy=dydt=−aωsinωtax=d2xdt2=−aω2sinωt and ay=d2ydt2=−aω2cosωtThus it is a clock-wise direction.

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