Consider a 20 kg uniform circular disk of radius 0.2 m. It is pin supported at its center and is at rest initially. The disk is acted upon by a constant force F=20 N through a mass less string wrapped around its periphery as shown in the figure.
Suppose the disk makes n number of revolutions to attain an angular speed of $50 r a d s^{- 1} .$ The value of n, to the nearest integer, is……………. [Given : In one complete revolution, the disk rotates by 6.28 rad]

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answer is 20.

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Detailed Solution

$\begin{array}{l} τ_{c} = 20 (0.2) = I α = \frac{20 {(0.2)}^{2}}{2} α \\ \Rightarrow α = 10 r a d / S^{2} \\ ω^{2} - {ω_{o}}^{2} = 2 α θ \\ 50^{2} - 0 = 2 (10) θ \\ θ = \frac{2500}{20} = 125 = n (2 π) \\ n = \frac{125}{6.28} = 19.9 ≅ 20 \end{array}$