A ring of radius r made of wire of density ρ is rotated about a stationary vertical axis passing through its centre and perpendicular to the plane of the ring as shown in figure. Find the percentage c

Question

A ring of radius r made of wire of density ρ is rotated about a stationary vertical axis passing through its centre and perpendicular to the plane of the ring as shown in figure. Find the percentage change in tension for two percent increase in angular velocity of rotation. Ignore gravity.

TestHub · Accepted Answer

For a rotating ring, an element subtending 2 θ : 2 T sin θ = ( ρ A ⋅ 2 θ r ) r ω 2 T = ρ A r 2 ω 2 ( s i n θ θ ​ ) , i.e. T ∝ ω 2 For 2% increase in ω : T Δ T ​ = 2 × 2% = 4%

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