question_answer

A rope is wound around a hollow cylinder of mass 3 kg and radius 40 cm. What is the angular acceleration of the cylinder if the rope is pulled with a force of 30 N?            

A) \[~5\text{ }m/{{s}^{2}}\]                             

B) \[~25\text{ }m/{{s}^{2}}\]

C) \[~0.25\text{ }rad/{{s}^{2}}\]    

D)  \[~25\text{ }rad/{{s}^{2}}\]

Correct Answer: D

Solution :

                  \[\tau =l\alpha \] \[F\times R=M{{R}^{2}}\alpha \] \[30\times 0.4=3\times {{(0.4)}^{2}}\alpha \] \[12=3\times 0.16\,\alpha \] \[400=16\alpha \] \[\alpha =25\,rad/{{s}^{2}}\]