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Question

# A particle moves in xy plane according to the law x=asinωt and y=a(1−cosωt) where a and ω are constants.The particle traces

A
a parabola
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B
a straight line equally inclined to x and y axis
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C
a circle
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D
a distance proportional to time
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Solution

## The correct options are C a circle D a distance proportional to timeA particle moves in xy plane according to the law x=asin(ωt) and y=a(1−cos(ωt)) where a and ω are constants.⇒sin2(ωt)=x2a2⇒cos2(ωt)=(1−ya)2⇒x2a2+(1−ya)2=1⇒x2+(y−a)2=a2The given equation is the equation of circle with centre (0,a), the radius aalso the angular velocity is ω so distance covered=aωt

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