An arc of radius 6m subtends an angle 120∘ at the centre. If an ant travels on the arc from one end to another end in 4sec, what will be the magnitude of average velocity of the ant ?
A
2m/s
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B
√32m/s
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C
3m/s
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D
3√32m/s
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Solution
The correct option is D3√32m/s Velocityavg=DisplacementTime taken
From the diagram,
The displacement of ant is AB.
Now from ΔAOB, draw the perpendicular bisector OD on AB ⇒AB=OAsin60∘+OBsin60∘ ∵OA=OB=r ⇒AB=2OAsin60∘ ⇒AB=2rsin60∘=2×6×√32=6√3m
Time taken to complete journey is Δt=4s
Hence, Velocityavg=6√3m4s ∴Velocityavg=3√32m/s