A spool of mass M = 3 kg and radius R = 20 cm has an axle of radius r = 10 cm around which a string is wrapped. The moment of inertia about an axis perpendicular to the plane of the spool and passing through the centre is M R 2 2 . If the coefficient of friction between the surface and the spool is 0 . 4 then the maximum tension which can be applied to the string for which the spool doesn't slip, is g = 10 m s - 2

Question

A spool of mass M = 3 kg and radius R = 20 cm has an axle of radius r = 10 cm around which a string is wrapped. The moment of inertia about an axis perpendicular to the plane of the spool and passing through the centre is M R 2 2 . If the coefficient of friction between the surface and the spool is 0 . 4 then the maximum tension which can be applied to the string for which the spool doesn't slip, is g = 10 m s - 2, 24 N, 18 N, 9 N, 36 N

MARKS App · Accepted Answer

Writing the torque about the instantaneous axis of rotation we get, τ = T × R - r = M R 2 2 + M R 2 α ⇒ T = 3 M R 2 2 R - r a R Also, T - μ M g = M a Substituting the values and solving for T we get, T = 18 N

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