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A uniform solid cylinder of mass m, radius R and length $l$ is on a rough surface. It is pulled by constant horizontal F acting at top of cylinder on one end as shown in the figure. The cylinder rolls without slipping. Choose the correct option(s):

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The acceleration of centre of mass $= \frac{4 F}{3 m}$

Net force of friction on cylinder $= \frac{F}{3}$

Net torque of frictional force about centre of mass is $\frac{F}{3} R \hat{j} - \frac{F l}{2} \hat{k}$

Net torque of applied force about O is $F R \hat{j}$

answer is A, B, C.

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Detailed Solution

Applying $τ = I α$ about y-axis
$F R - f R = \frac{1}{2} M R^{2} α = \frac{1}{2} M a_{C} R$
$F + f = M a_{c}$
$a_{c} = \frac{4 F}{3 m}$

${\vec{τ}}_{n e t} = F R (- \hat{j}) + {\vec{τ}}_{f} + F \frac{l}{2} \hat{k} = \frac{2 F R}{3} (- \hat{j})$

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