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JEE Main & Advanced Sample Paper JEE Main - Mock Test - 28

  • 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 \[8 rad {{s}^{-}}^{2}\] is produced in it due to the torque. Then, moment of inertia of the wheel is \[\left( g = 10 m{{s}^{-}}^{2} \right)\]

    A) \[2 kg-{{m}^{2}}\]                  

    B) \[1 kg-{{m}^{2}}\]

    C) \[4 kg-{{m}^{2}}\]                  

    D) \[8 kg-{{m}^{2}}\]

    Correct Answer: A

    Solution :

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


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