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A uniform steel rod of cross-sectional area A and length L is suspended so that it hangs vertically. The stress at the middle point of the rod is ( $ρ$ is the density of the material)

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$\frac{1}{2} ρ g L$

$\frac{1}{4} ρ g L$

$ρ g L$

None of these

answer is A.

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Detailed Solution

Force at the midpoint $\frac{m g}{2}$

$s t r e s s = \frac{m g}{2 A} = \frac{l A ρ g}{2 A} = \frac{l ρ g}{2}$

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