Question

# The radii and Young's modulus of two uniform wires $$A$$ & $$B$$ are in the ratio $$2:\ 1$$ and $$1:\ 2$$ respectively. Both the wires are subjected to the same longitudinal force. If increase in the length of wire $$A$$ is $$1\%$$ . Then the percentage increase in length of wire $$B$$ is :

A
1
B
1.5
C
2
D
3

Solution

## The correct option is C $$2$$$$Y = \dfrac{F/A}{\triangle l/l}$$$$\triangle l = \dfrac{F l}{\pi r^{2}Y}$$$$\triangle l_{A} = \dfrac{F l}{\pi r_{A}^{2}Y_{A}} .............(1)$$$$\triangle l_{B} = \dfrac{F l}{\pi r_{B}^{2}Y_{B}} .............(2)$$Dividing  1  by  2$$\dfrac{\triangle l_{A}}{\triangle l_{B}} =\dfrac{r_{B}^{2}Y_{B}}{r_{A}^{2}Y_{A}} = (\dfrac{r_{B}}{r_{A}})^{2} (\dfrac{Y_{B}}{Y_{A}}) = (\dfrac{1}{2})^{2} (\dfrac{2}{1}) = \dfrac{1}{2}$$$$\triangle l_{B} = 2\triangle l_{A} = 2 \times 1$$ %$$= 2$$ %Physics

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