AB is a light rigid rod, which is rotating about a vertical axis passing through end A . A spring of force constant k and natural length l is attached at A and its other end is attached to a small bead of mass m . The bead can slide without friction on the rod. At the initial moment, the bead is at rest (w.r.t the rod) and the spring is unstretched. Select incorrect options :

Question

AB is a light rigid rod, which is rotating about a vertical axis passing through end A . A spring of force constant k and natural length l is attached at A and its other end is attached to a small bead of mass m . The bead can slide without friction on the rod. At the initial moment, the bead is at rest (w.r.t the rod) and the spring is unstretched. Select incorrect options :, V max = m ω 2 l 2 k - m ω 2, V max = m ω 4 l 2 k - m ω 2, V max = m ω 4 l 2 m ω 2 - k, V max = m ω 2 l 2 m ω 2 - k

MARKS App · Accepted Answer

Velocity will be maximum at the equilibrium position ⇒ k x = m ω 2 l + x ⇒ x = m ω 2 l k - m ω 2 Now, using work-energy theorem ∆ K E = Work done by all the forces 1 2 m V max 2 = ∫ 0 x m ω 2 l + x d x - 1 2 k x 2 ⇒ V max 2 = 2 m ω 2 l x + m ω 2 x 2 - k x 2 m V max 2 = m ω 2 l + m ω 2 l + x - k x x m = m ω 2 l x m ⇒ V max 2 = ω 2 l x = m ω 4 l 2 k - m ω 2 V max = m ω 4 l 2 k - m ω 2

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