A rod of length l ⁡ = 2 m is maintained to rotate with a constant angular velocity ω = 1 rad s - 1 about a vertical axis passing through one end (diagram). There is a spring constant k = 1 N m - 1 which just encloses rod inside it in natura

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A rod of length l ⁡ = 2 m is maintained to rotate with a constant angular velocity ω = 1 rad s - 1 about a vertical axis passing through one end (diagram). There is a spring constant k = 1 N m - 1 which just encloses rod inside it in natural length. One end of the spring is attached to the axis of rotation. S is a sleeve of mass m = 1 kg which can just fit on rod. All surfaces are smooth. With what minimum kinetic en

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Correct answer: 6

For entering without jerk v 2 = l ⁡ ω 0 = 2 m s - 1 Using work-energy theorem on the sleeve after entering in the frame of rod W spring + W centrifugal = Δ K - 1 2 k l ⁡ 2 - 1 2 m ω 2 l ⁡ 2 = 0 - 1 2 mv 1 2 ⇒ v 1 2 = 8 Now, K = 1 2 m v 1 2 + v 2 2 = 6

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