Two wires AC and BC are each tied to a sphere at C. AB=0.2m the sphere is made to revolve in a horizontal circle at a constant speed v. Then, when both wires are taut.
A
vmin=1m/s
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B
vmin=2m/s
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C
vmax=√3m/s
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D
vmax=4m/s
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Solution
The correct options are Avmin=1m/s Cvmax=√3m/s For vertical equilibrium, T1cos30∘+T2cos60∘=mg √3T1+T2=2mg...(1) The net force along the horizontal direction provides the centripetal force for circular motion. T1cos30∘+T2cos60∘=mv2r T1+√3T2=2mv2r...(2) From (1) and (2), T2=√3mv2r−mg,T1=√3mg−mv2r
Here AB=BC=0.2,r=(√32×0.2)m The string is taut, if T2>0,vmin=√gr√3=1m/s T1>0,vmax=√√3gr=√√3×10×√3×0.1=√3m/s