A disc of radius 10cm is rotating about the central axis perpendicular to its plane. A force of 5N acts on it tangentially. The disc was initially at rest. Calculate the value of power supplied by the force when the disc has rotated by 30°.The mass of the disc is 2kg.(a) 1.28W(b) 1.8W(c) 3.9W(d) 2.63WThe question was posed to me in exam.The doubt is from Dynamics of Rotational Motion about a Fixed Axis in section System of Particles and Rotational Motion of Physics – Class 11

A disc of radius 10cm is rotating about the central axis perpendicular

1.	A disc of radius 10cm is rotating about the central axis perpendicular to its plane. A force of 5N acts on it tangentially. The disc was initially at rest. Calculate the value of power supplied by the force when the disc has rotated by 30°.The mass of the disc is 2kg.(a) 1.28W(b) 1.8W(c) 3.9W(d) 2.63WThe question was posed to me in exam.The doubt is from Dynamics of Rotational Motion about a Fixed Axis in section System of Particles and Rotational Motion of Physics – Class 11
Answer» Correct choice is (b) 1.8W Easy explanation: Work done = Tθ, where T is torque & θ is angular displacement.T = rF = 0.15 = 0.5Nm & θ = 30° = π/6 rad. ∴ Work = 0.5π/6 = π/12 J. Moment of INERTIA about SPINNING AXIS = MR^2/2 = 20.01/2 = 0.01kgm^2. Using, T = Ia, where ‘I’ is moment of inertia & ‘a’ is angular acceleration, we get: a = T/I ∴ a = 0.5/0.01 = 50 rad/s^2. Now, θ = w0t + (1/2)at^2 to calculate the time for 30° rotation, where wo is initial angular velocity. ∴ π/6 = 0 + 0.550t^2. ∴ t = √(π/150) = 0.145 s. ∴ POWER = Work/time = (π/12) / (0.145) = 1.8 W.

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