Question

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. $\frac{7}{36}ML^{2}$
• B. $\frac{7}{48}ML^{2}$
• C. $\frac{11}{48}ML^{2}$
• D. $\frac{ML^{2}}{12}$

Answer 1

Answer: (B)

$\frac{7}{48}ML^{2}$

Answer 2

Moment of inertia of a uniform rod of length $L$ and mass $M$ about an axis passing through the centre and perpendicular to its length is given by $I_0 = \frac{ML^{2}}{12}$ ..(i) According to the theorem of parallel axes, 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 given by $I = I_{0} +M \left(\frac{L}{4}\right)^{2} = \frac{ML^{2}}{12} +\frac{ML^{2}}{16} = \frac{7ML^{2}}{48}$ (Using (i))