Question

A rod of mass $m$, uniform cross sectional area $A$ and length $L$ is accelerated by applying force $F$ as shown in figure on a smooth surface. If Young's modulus of elasticity of the material of rod is $Y$. (Consider $x$ as measured from the right end).

• A. Tension in rod as a function of distance $x$ is $\frac{Fx}{2L}$
• B. Strain in rod is $\frac{F}{2AY}$
• C. Elastic potential energy stored in the rod is $\frac{F^{2}L}{8AY}$
• D. There is no stress in rod

Answer 1

Answer: (A), (B)

The correct options are
A Tension in rod as a function of distance $x$ is $\frac{Fx}{2L}$
B Strain in rod is $\frac{F}{2AY}$

$a=\frac{F}{m}$

$\begin{array}{c}T=m_{BC}\times a\\ T=\frac{m}{L}\times x\times \frac{F}{m}\Rightarrow T=\frac{F\times x}{L}\\ \text{Strain}=\frac{\Delta l}{L}\\ \frac{dL}{dx}=\frac{Fx}{LAY}\\ \int dL={\int }_0^L\frac{Fx}{LAy}dx\Rightarrow \Delta L=\frac{FL}{2Ay}\end{array}$

$\frac{\Delta L}{L}=\frac{F}{2AY}$

Hence option A and B is correct