question_answer

Moment of inertia of a uniform rod of length L and mass M, about an axis passing through L/4 from one end and perpendicular to its length is:

A) \[\frac{7}{36}{{\operatorname{ML}}^{2}}\] 

B)              \[\frac{7}{48}{{\operatorname{ML}}^{2}}\]

C) \[\frac{11}{48}{{\operatorname{ML}}^{2}}\]               

D)  \[\frac{{{\operatorname{ML}}^{2}}}{12}\]

Correct Answer: B

Solution :

Apply parallel axis theorem \[{{\operatorname{I}}_{P}}={{I}_{C}}+M{{\left( \frac{L}{4} \right)}^{2}}\] \[{{\operatorname{I}}_{P}}=\frac{M{{L}^{2}}}{12}+\frac{M{{L}^{2}}}{16}\] \[{{\operatorname{I}}_{P}}=\frac{7}{48}M{{L}^{2}}\]