Question

Work done in streatching uniform rod of length $L$ and area of crossection $A$ by small amount $x$ is
[$Y$ is youngs modulus]

• A. $\frac{YAx}{4}$
• B. $\frac{3YA{x}^2}{2L}$
• C. $\frac{YA{x}^2}{2L}$
• D. $\frac{Y{A}^{2}x}{2L}$

Answer 1

The correct option is C $\frac{YA{x}^2}{2L}$


Work =$\int Fdx$

& $Y=\frac{FL}{Ax}\Rightarrow F=\frac{YA}{L}x$

so Work =$\frac{1}{2}\frac{YA}{L}{x}^2$