Subjective Type

Two persons pull a rope towards themselves. Each person exerts a force of $$100$$ $$N$$ on the rope. Find the Young modulus of the material of the rope if it extends in length by $$1$$ $$cm$$. Original length of the rope is $$2$$ $$m$$ and the area of cross section is $$2$$ $$cm^2$$

Solution

The young's modulus of the rod is defined as:
$$Y=\cfrac{Stress}{Strain}$$

The stress is defined as:
$$stress=\dfrac{Load}{Area}$$

And the strain is defined as:
$$strain=\dfrac{L}{\Delta L}$$

Substituting the values of strss and strain:
$$Y=\cfrac{{Load/Area}}{{\Delta L/L}}$$

$$\Rightarrow Y=\cfrac{{100/2cm^2}}{{1cm/2m}}$$

$$\Rightarrow Y=\cfrac{50\times 10^4}{0.5\times 10^{-2}}$$

$$\Rightarrow Y=10^8$$ $${N/m^2}$$

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