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Question

In a situation shown in figure, if the length of the minute's hand is 10π cm, find the magnitude of change in velocity of the tip of the minute's hand.


A
13 cm/min
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B
3 cm/min
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C
2 cm/min
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D
12 cm/min
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Solution

The correct option is A 13 cm/min
For one complete revolution of minute hand, θ=2π radians
For 20 minutes, θ=2π60×20=2π3 radians
Magnitude of change in velocity
|v2v1|=v22+v212v2v1 cos θ
For uniform circular motion, v1=v2=v
|v2v1|=v2+v22v2 cos 2π3=3v=3rω
( v=rω)

To find ω:
ω=ΔθΔt=2π320=π30 rad/min.
|v2v1|=3×10π×π30=13 cm/min.

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