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  4. The rope shown in the figure is wound around a uniform cylinder of mass 4 kg , about the axis of the cylinder. If the cylinder rolls without slipping, then the linear acceleration of its centre of mass is <img class=img-fluid question-image alt=Question src=https://cdn.tardigrade.in/q/nta/p-uoclavwihxdq.png />

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Q. The rope shown in the figure is wound around a uniform cylinder of mass $4 \, kg$ , about the axis of the cylinder. If the cylinder rolls without slipping, then the linear acceleration of its centre of mass is

Question

NTA AbhyasNTA Abhyas 2020System of Particles and Rotational Motion

Solution:

For rotational motion
$\tau=I\alpha $
$\Rightarrow F\left(2 R\right)=\frac{3}{2}MR^{2}\left(\frac{a}{R}\right)$
$\Rightarrow a=\frac{4 F}{3 M}=\frac{4 \left(20\right)}{3 \left(4\right)}=6.7 \, m \, s^{- 2}$