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  • 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 massless string wrapped around its periphery as shown in the figure. <img

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 massless string wrapped around its periphery as shown in the figure. Suppose the disk makes a 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]
Option: 1 20
Option: 2 30
Option: 3 40
Option: 4 50

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\\\alpha=\frac{\tau}{\mathrm{I}}=\frac{\mathrm{F} . \mathrm{R} .}{\mathrm{mR}^{2} / 2}=\frac{2 \mathrm{~F}}{\mathrm{mR}} \\ \\ \Rightarrow \alpha=\frac{2 \times 200}{20 \times(0.2)}=10 \mathrm{rad} / \mathrm{s}^{2}

\begin{array}{l} \omega^{2}=\omega_{0}^{2}+2 \alpha \Delta \theta \\ \Rightarrow (50)^{2}=0^{2}+2(10) \Delta \theta \\ \Rightarrow \Delta \theta=\frac{2500}{20} \\ \Delta \theta=125 \mathrm{rad} \\ \Rightarrow \text { No. of revolution }=\frac{125}{2 \pi} \approx 20 \text { revolution } \end{array}

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