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Physics · SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
हिन्दीA rope of negligible mass is wound round a hollow cylinder of mass \( 3 \text{ kg} \) and radius \( 40 \text{ cm} \). If the rope is pulled with a constant force of \( 30 \text{ N} \), assuming the cylinder rotates about its standard axis without slipping, the angular acceleration of the cylinder and the linear acceleration of a point on the rope are:
Correct answer · Option 1
\( 25 \text{ rad s}^{-2} \) and \( 10 \text{ m s}^{-2} \)
Explanation
Torque \( \tau = F R = 30 \times 0.4 = 12 \text{ N m} \). For a hollow cylinder, \( I = MR^2 = 3 \times (0.4)^2 = 0.48 \text{ kg m}^2 \). \( \alpha = \frac{\tau}{I} = \frac{12}{0.48} = 25 \text{ rad s}^{-2} \). Linear acceleration \( a = R\alpha = 0.4 \times 25 = 10 \text{ m s}^{-2} \).
