A) \[({{m}_{w}}+{{m}_{b}}){{L}^{2}}/12\]
B) \[({{m}_{w}}+{{m}_{b}}){{L}^{2}}/6\]
C) \[({{m}_{w}}+{{m}_{b}}){{L}^{2}}/3\]
D) \[({{m}_{w}}+{{m}_{b}}){{L}^{2}}/2\]
Correct Answer: A
Solution :
Moment of inertia \[{{M}_{1}}={{m}_{w}}\times \frac{{{(L/2)}^{2}}}{3}={{m}_{w}}\frac{{{L}^{2}}}{12}\] Moment of inertia \[{{M}_{2}}={{m}_{b}}\times \frac{{{(L/2)}^{2}}}{3}={{m}_{b}}\times \frac{{{L}^{2}}}{12}\] Moment of inertia \[M={{M}_{1}}+{{M}_{2}}\] \[={{m}_{w}}\frac{{{L}^{2}}}{12}+{{m}_{b}}\times \frac{{{L}^{2}}}{12}\] \[=({{m}_{w}}={{m}_{b}})\frac{{{L}^{2}}}{12}\]You need to login to perform this action.
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