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Q.

Consider a 20 kg uniform circular disc 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 massless string wrapped around its periphery as shown in the figure.

Suppose the disc 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

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

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Consider a 20 kg uniform circular disc 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 massless string wrapped around its periphery as shown in the figure. Suppose the disc makes n number of revolutions to attain an angular speed of 50 rad s-1.The value of n, to the nearest integer, is…………….[Given : In one complete revolution, the disk rotates by 6.28 rad]