A string is wound a hollow cylinder of mass 5 kg and radius 0.5m. 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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20 rad/s²

16 rad/s²

12 rad/s²

10 rad/s²

answer is B.

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Detailed Solution

Pure rolling condition, $a = αR$

Translation Motion, $40 + f = m (Rα)$

Rotational Motion, $40 \times R - f \times R = Iα$

After Solving,

$α = \frac{40}{mR} = 16 {rads}^{- 2}$

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