question_answer

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

A) \[6.7\text{ }m/{{s}^{2}}\]                     

B) \[10\text{ }m/{{s}^{2}}\]            

C) \[\text{3}\text{.3 }m/{{s}^{2}}\]           

D) None of these    

Correct Answer: A

Solution :

Let friction force = f

\[F+f=ma\]              ...(i)

\[(F-f)R=I\alpha \]                   ...(li)

From \[e{{q}^{n}}s,\] (i) and (ii),

\[2F=ma+\frac{I\alpha }{R}\]

Use \[\alpha =\frac{a}{R}\]  (for pure rolling)

\[2F=ma+\frac{Ia}{{{R}^{2}}}\]

\[40=4a+\frac{0.02a}{{{(0.1)}^{2}}};\]  \[a=\frac{40}{6}=6.7\,m/{{s}^{2}}\]