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Question

The seconds hand of a watch has length 6 cm. Speed of the end point and magnitude of difference in velocities at positions A and B, as shown in the figure will be


A
2π mms, 22π mms
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B
π mms, 22π mms
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C
2π mms, 2π mms
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D
π mms, 2π mms
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Solution

The correct option is A 2π mms, 22π mms
We know that speed is given as
v=Rω=R(2πt)
=60 mm×2π60
=2π mm/s

Since it performs uniform circular motion, change in velocity can be given as
|Δv|=v2+v22v×vcosθ
θ=90=π2 rad
|Δv|=v2+v22v×vcos(π2)=2v
|Δv|=22π mm/s

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