Consider a 20 kg uniform circular disk of radius 0.2 m. It is pin… | JEE Main 2021 (16 Mar, Shift 1)

Q42JEE Main 2021 · 16 MAR · SHIFT 1Medium

Rotational Kinematics & Dynamics

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 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]

Numerical answer type. Work it out, then open the answer.

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Answer: 20

$I = \frac{1}{2}MR^2 = \frac{1}{2}(20)(0.2)^2 = 0.4\text{ kg m}^2$ , $\tau = FR = 20\times0.2 = 4\text{ N m}$
$\alpha = \frac{\tau}{I} = 10\text{ rad/s}^2$
$\theta = \frac{\omega^2}{2\alpha} = \frac{2500}{20} = 125\text{ rad}$
$n = \frac{125}{6.28} \approx 20$ revolutions.

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