Length of the minute hand in a clock is 10cm. Find difference between average speed and magnitude of average velocity (in cm/min) of tip of the minute hand from 6 a.m. to 6:20 a.m.
A
2π3−√32
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B
2π3−12
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C
π3−√32
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D
π3−12
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Solution
The correct option is Cπ3−√32
Given time, t=20min The distance covered by minute hand d=rθ, where r is the length of the minute hand and θ in radians.
θ=120∘=π180×120rad=2π3rad d=10×2π3cm Average speed: v=dt=20π3×20=π3cm/min
Displacement: D=2rsinθ2 D=2×10×sin1202=10√3cm Magnitude of average velocity: V=Dt=10√320=√32cm/min