Question

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) 2.63W

The 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 1

Correct choice is (b) 1.8W

Easy explanation: Work done = Tθ, where T is torque & θ is angular displacement.                                                                                    T = r*F = 0.1*5 = 0.5Nm

& θ = 30° = π/6 rad.

∴ Work = 0.5*π/6 = π/12 J.

Moment of inertia about spinning axis = MR^2/2 = 2*0.01/2 = 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 + 0.5*50*t^2.

∴ t = √(π/150) = 0.145 s.

∴ Power = Work/time = (π/12) / (0.145) = 1.8 W.