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Question

Length of the minute hand in a clock is 10 cm. 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
2π332
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B
2π312
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C
π332
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D
π312
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Solution

The correct option is C π332

Given time, t=20 min
The distance covered by minute hand
d=rθ, where r is the length of the minute hand and θ in radians.

θ=120=π180×120 rad=2π3 rad
d=10×2π3 cm
Average speed:
v=dt=20π3×20=π3 cm/min

Displacement: D=2rsinθ2
D=2×10×sin1202=103 cm
Magnitude of average velocity:
V=Dt=10320=32 cm/min

The difference is : π332 cm/min

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