Question

Two long thin rods of length L and nL are made of the same material and have a same cross-section. If the longer rod has MI about the transverse symmetry axis 125 times that of the shorter rod, the value of n is :

• A. 2
• B. 4
• C. 5
• D. 8

Answer 1

The correct option is C 5

$\begin{array}{c}\text{Let, there are two rods}A\text{and}B\text{of same material, length}\\ L\text{and}nL\text{respectively.}\\ \text{Thus,}{m}_A=m\text{and}{m}_B=nm\text{.}\end{array}$

$\begin{array}{c}\text{Now, moment of inertia about transverse symmetry}axis=\frac{m{l}^2}{12}\text{,}\\ \text{Given,}{I}_B=125.I_A\\ \Rightarrow \left(nm\right)(nL{)}^2/12=125\times \frac{m{L}^2}{12}.\\ \Rightarrow n=5\end{array}$