question_answer

A tangential force of 20 N is applied on a cylinder of mass 4 kg and moment of    inertia \[0.02\,kg\,{{m}^{2}}\] about its own axis. If the cylinder rolls without slipping, then linear acceleration of its centre of mass will be

A) \[6.7m/{{s}^{2}}\]         

B)        \[10m/{{s}^{2}}\]

C) \[3.3m/{{s}^{2}}\]         

D)        None of these

Correct Answer: A

Solution :

[a] Let friction force = f \[F+f=ma\]          ? (i) \[(F-f)R=I\alpha \]      ? (ii) \[From\,\,\,e{{q}^{n}}s.\,(i)\,and\,(ii),\] \[2F=ma+\frac{I\alpha }{R}\] \[Use\,\alpha =\frac{a}{R}\] (for pure rolling) \[2F=ma+\frac{Ia}{{{R}^{2}}}\] \[40=4a+\frac{0.02a}{{{(0.1)}^{2}}};a=\frac{40}{6}=6.7m/{{s}^{2}}\]