A thin ring of radius R is made of a material of density ρ and Young's modulus Y. If the ring is rotated about its centre in its own plane with angular velocity ω, then -
(′A′ is cross-section of ring)
A
Tension produced in the ring, T=Aρω2R2
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B
Tension produced in the ring, T=Aρω2R
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C
Small increase in its radius, ΔR=ρω2R3Y
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D
Small increase in its radius, ΔR=ρω2R22Y
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Solution
The correct option is C Small increase in its radius, ΔR=ρω2R3Y
Consider an element PQ of length dl.
Let T be the tension in the wire.
Now, mass of element PQ,
⇒dm=A(dl)ρ
The component of T towards the centre, provides the necessary centripetal force.