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Question

# A table clock has its minute hand 4 cm long. Find the average velocity of the tip of the minute hand (a) between 6 AM to 6:30 AM and (b) between 6 AM to 6:30 PM

A
4×103cms,1.8×104cms
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B
4.4×103cms,1.8×104cms
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C
0.44×103cms,1.8×104cms
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D
4.4×103cms,0.18×104cms
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Solution

## The correct option is B 4.4×10−3cms,1.8×10−4cmsAt 6 AM the tip of the minute hand is at 12 mark and at 6:30 AM or 6:30 PM it is 180∘ away. Thus, the straight-line distance between the initial and final positions of the tip of minute hand is equal to the diameter of the clock. Displacement =2×R=2×4 cm=8 cm The displacement is from 12 mark to 6 mark on the clock panel. This is also the direction of the average velocity in both the cases. Therefore, (a) The time taken from 6 AM to 6:30 AM is 30 min=1800 s. The average velocity is vav=DisplacementTime=81800=4.4×10−3 cms (b) The time taken from 6 AM to 6:30 PM is 12.5 hr=45000 s. The average velocity is vav=DisplacementTime=845000=1.8×10−4 cms

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