A uniform wire has length ' $\mathrm{L}^{\prime}$ and weight ' $\mathrm{W}^{\prime}$. One end of the wire is attached rigidly to a point in the roof and weight ' $\mathrm{W}_{1}{ }^{\prime}$ is suspended from its lower end. If ' $\mathrm{A}^{\prime}$ is the cross-sectional area of the wire then the stress in the wire at a height $\frac{3 \mathrm{~L}}{4}$ from its lower end isA)$\frac{4 \mathrm{~W}_{1}+3 \mathrm{~W}}{4 \mathrm{~A}}$B)$\frac{3 \mathrm{~W}_{1}-4 \mathrm{~W}}{2 \mathrm{~A}}$C)$\frac{3 \mathrm{~W}_{1}+4 \mathrm{~W}}{2 \mathrm{~A}}$D)$\frac{4 \mathrm{~W}_{1}-3 \mathrm{~W}}{4 \mathrm{~A}}$

Home » A uniform wire has length ‘ and weight ‘ . One end of the wire is attached rigidly to a point in the roof and weight ‘ is suspended from its lower end. If ‘ is the cross-sectional area of the wire then the stress in the wire at a height from its lower end isA)B)C)D)

A uniform wire has length ‘ $\mathrm{L}^{\prime}$ and weight ‘ $\mathrm{W}^{\prime}$ . One end of the wire is attached rigidly to a point in the roof and weight ‘ $\mathrm{W}_{1}{ }^{\prime}$ is suspended from its lower end. If ‘ $\mathrm{A}^{\prime}$ is the cross-sectional area of the wire then the stress in the wire at a height $\frac{3 \mathrm{~L}}{4}$ from its lower end is
A) $\frac{4 \mathrm{~W}_{1}+3 \mathrm{~W}}{4 \mathrm{~A}}$
B) $\frac{3 \mathrm{~W}_{1}-4 \mathrm{~W}}{2 \mathrm{~A}}$
C) $\frac{3 \mathrm{~W}_{1}+4 \mathrm{~W}}{2 \mathrm{~A}}$
D) $\frac{4 \mathrm{~W}_{1}-3 \mathrm{~W}}{4 \mathrm{~A}}$

Physics

A uniform wire has length ‘ $\mathrm{L}^{\prime}$ and weight ‘ $\mathrm{W}^{\prime}$ . One end of the wire is attached rigidly to a point in the roof and weight ‘ $\mathrm{W}_{1}{ }^{\prime}$ is suspended from its lower end. If ‘ $\mathrm{A}^{\prime}$ is the cross-sectional area of the wire then the stress in the wire at a height $\frac{3 \mathrm{~L}}{4}$ from its lower end is
A) $\frac{4 \mathrm{~W}_{1}+3 \mathrm{~W}}{4 \mathrm{~A}}$
B) $\frac{3 \mathrm{~W}_{1}-4 \mathrm{~W}}{2 \mathrm{~A}}$
C) $\frac{3 \mathrm{~W}_{1}+4 \mathrm{~W}}{2 \mathrm{~A}}$
D) $\frac{4 \mathrm{~W}_{1}-3 \mathrm{~W}}{4 \mathrm{~A}}$

Correct option is A.

$\text { stress }=\frac{\text { Tension }}{\text { Area }}$
Tension at height $\frac{3 \mathrm{~L}}{4}$ from lower end
$\text { is } \frac{3}{4} \mathrm{w}+\mathrm{w}_{1}$
So, stress $=\frac{\frac{3}{4}W+\mathrm{w}_{1}}{\mathrm{A}}$

i

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