Question

A metal rod of length $l$ is being pulled on a smooth horizontal surface as shown. $Y$ and $A$ denote Young's modulus and cross-sectional area of the rod respectively. Elongation in the rod is

• A. $\frac{Fl}{AY}$
• B. $\frac{2Fl}{AY}$
• C. $\frac{Fl}{2AY}$
• D. $\frac{Fl}{4AY}$

Answer 1

Answer: (A)

A. $\frac{Fl}{AY}$

Answer 2

The elongation ($\Delta L$) of a rod under tensile stress is given by the formula $\Delta L = \frac{FL}{AY}$, where $F$ is the applied force, $L$ is the original length, $A$ is the cross-sectional area, and $Y$ is Young's modulus. In this problem, the length is $l$. Therefore, the elongation is $\frac{Fl}{AY}$.