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Question

The magnitude of the displacement of a particle moving in a circle of radius a with constant angular speed ω varies with time t as 


A
2a sin ω t
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B
2a sin ω t2
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C
2a cos ω t
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D
2a cos ω t2
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Solution

The correct option is B 2a sin ω t2
In time t, particle has rotated an angle θ=ω t



From ORQ
OR=acosθ,QR=asinθ
PR=OPOR=aacosθ

Displacement of the particle
S=PQ=QR2+PR2
S=(a sin ω t)2+(aa cos ω t)2
S=a(sin ω t)2+(cos ω t)2+12cos ω t
S=a22cos ω t
S=a2(1cos ω t)
S=a4(sin ω t2)2​​​​​​​​​​​​​​
s=2asin ω t2
Hence, the correct answer is option (b).

Physics

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