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  4. A string is wound around a hollow cylinder of mass 5 kg and radius 0.5 m. If the string is now pulled with a horizontal force of 40 N, and the cylinder is rolling without slipping on a horizontal surface (see figure), then the angular acceleration of the cylinder will be (Neglect the mass and thickness of the string) :

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Q. A string is wound around a hollow cylinder of mass $5\, kg$ and radius $0.5\, m$. If the string is now pulled with a horizontal force of $40\, N$, and the cylinder is rolling without slipping on a horizontal surface (see figure), then the angular acceleration of the cylinder will be (Neglect the mass and thickness of the string) :Physics Question Image

JEE MainJEE Main 2019System of Particles and Rotational Motion

Solution:

$40 + f = m(R \alpha)$ .....(i)
$40 \times R - f \times R = mR^2 \alpha $
$40 - f = mR \alpha$ ...... (ii)
From (i) and (ii)
$\alpha = \frac{40}{mR} = 16 $

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