Which of the following curve represents the correctly distribution of elongation $(y)$ along heavy rod under its own weight $L \rightarrow$ length of rod, $x \rightarrow$ distance of point from lower end?
- A
- B
- C
- D
Medium
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For elongation of rod under its own weight
We know $\Delta x=\frac{\rho g x^2}{2 Y}$ $\left\{\begin{array}{l}\text { Where, } \\ \Delta x=\text { Elongation } \\ \rho=\text { Density of rod } \\ Y=\text { Young's modulus } \\ L=\text { Length } \\ g=\text { Acceleration due to gravity } \\ x=\text { Distance of point from lower end }\end{array}\right.$
We can clearly see that elongation $\propto\left(x^2\right)$
So graph of $\Delta x$ vs $x$ should be a upward parabola.
We know $\Delta x=\frac{\rho g x^2}{2 Y}$ $\left\{\begin{array}{l}\text { Where, } \\ \Delta x=\text { Elongation } \\ \rho=\text { Density of rod } \\ Y=\text { Young's modulus } \\ L=\text { Length } \\ g=\text { Acceleration due to gravity } \\ x=\text { Distance of point from lower end }\end{array}\right.$
We can clearly see that elongation $\propto\left(x^2\right)$
So graph of $\Delta x$ vs $x$ should be a upward parabola.
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