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Question

$$A$$ and $$B$$ are two wires. The radius of $$A$$ is twice that of $$B$$. They are stretched by the same load. Then the stress on $$B$$ is 


A
equal to that on A
loader
B
four times that on A
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C
two times that on A
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D
half that on A
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Solution

The correct option is B four times that on $$A$$
$$stress=\dfrac{Force}{Area}$$
$$\therefore \displaystyle stress \propto \dfrac{1}{\pi r^2}$$
Thus, $$\dfrac{S_B}{S_A}=\left[\dfrac{r_A}{r_B}\right]^2=(2)^2\Rightarrow S_B=4S_A$$

Physics

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