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  • The radius of gyration of a uniform rod of length l, about an axis passing through a point  away from the centre of the rod and perpendicular to it

The radius of gyration of a uniform rod of length l, about an axis passing through a point \frac{l}{4} away from the centre of the rod and perpendicular to it is:-  
Option: 1 \frac{1}{8}l

 
Option: 2 \sqrt{\frac{7}{48}l}

Option: 3 \sqrt{\frac{3}{8}l}  

Option: 4 \frac{1}{4}l
 

Answers (1)

best_answer

 

 

                  

Moment of inertia of rod about an axis perpendicular through COM

I_{COM}=\frac{Ml^2}{12}

And I_N=I_{COM}+M(\frac{l}{4})^2=\frac{Ml^2}{12}+M(\frac{l^2}{16})=\frac{7Ml^2}{48}

Radius of Gyration

\\ K=\sqrt{\frac{I_N}{M}}=\sqrt{\frac{7Ml^2}{48M}}=\frac{l}{4}*\sqrt{\frac{7}{3}} \\ = l\sqrt{\frac{7}{48}}

 

So the option (2) is correct.

Posted by

Ritika Jonwal

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