question_answer

A wheel of radius 0.4 m can rotate freely about its axis as shown in the figure. \[A\]String is wrapped over its rim and a mass of 4 kg is hung. An angular acceleration of \[8\text{ }rad-{{s}^{-2}}\] is produced in it due to the torque. Then, moment of inertia of the wheel is \[(g=10m{{s}^{-2}})\]

A)  \[2\text{ }kg-{{m}^{2}}\]

B)  \[1\text{ }kg-{{m}^{2}}\]

C)  \[4\text{ }kg-{{m}^{2}}\]

D)  \[8\text{ }kg-{{m}^{2}}\]

Correct Answer: A

Solution :

Given, \[r=0.4m,\] \[\alpha =8\,rad\,{{s}^{-1}},\] \[m=4kg,I=?\] Torque,        \[\tau =I\alpha \] \[mgr=I.\alpha \] or \[4\times 10\times 0.4=I\times 8\] \[\Rightarrow \] \[I=\frac{16}{8}=2kg.{{m}^{2}}\] or \[I=2kg.{{m}^{2}}\]