# Two circular bars A and B of same material are subjected to uniaxial loading. If the diameter and load acting on bar B is double than that of A, the r

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Two circular bars A and B of same material are subjected to uniaxial loading. If the diameter and load acting on bar B is double than that of A, the ratio of safety of bar B to A is
1. 2
2. $\frac 12$
3. $\frac 14$
4. 4

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Correct Answer - Option 1 : 2

Explanation:

Stress developed in bar(σ) = $\frac FA$

where F = Force/load applied, A = Cross-section Area

For same material bars

$Safety ∝\frac {1}{stress ~developed}$

In case of circular bar A

$\sigma_A =\frac FA$

In case of circular bar B

Area = 4A as diameter doubled and Area ∝ d2

load = 2F as force doubled

$\sigma_B =\frac {2F}{4A} = \frac 12\frac FA= \frac {\sigma _A}{2}$

∴ Ratio of safety of bar B to bar A= $\frac {\sigma _A}{\sigma _B}=\frac {\sigma _A}{\frac {\sigma _A}2}=2$

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