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A thin rod \mathrm{A B} (of mass \mathrm{m} and length \mathrm{l}) is sliding keeping in contact with a vertical wall and a smooth surface as shown. \mathrm{MI} of the rod about instantaneous axis of rotation at the instant shown is: -

Option: 1

\mathrm{\frac{m l^2}{3}}
 


Option: 2

\mathrm{\frac{m l^2}{6}}
 


Option: 3

\mathrm{\frac{m l^2}{6} \cos \theta}
 


Option: 4

\mathrm{\frac{m l^2}{6} \sin \theta}


Answers (1)

best_answer

From geometry, \mathrm{ d=\frac{l}{2} }

so,\mathrm{I_p =I_{c m}+m d^2 }

          \mathrm{ =\frac{m l^2}{12}+m \frac{l^2}{4} }            \mathrm{ \left\{\begin{array}{c} \because \quad M I \text { of } \text { rod }=\frac{M l^2}{12} \\ d=l / 2 \end{array}\right. }

          \mathrm{ I_p =\frac{m l^2}{3} }

Hence option 1 is correct.





 

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