A uniform wire of length of weight is suspended from the roof with a weight of at the other end. The stress in the wire

Question

A uniform wire of length $l$ of weight $w$ is suspended from the roof with a weight of $W$ at the other end. The stress in the wire at $\frac{l}{3}$ distance from the top is $(\frac{W}{A} + \frac{2 w}{γ A}),$ where $A$ is the cross-sectional area of the wire. The value of $γ$ is ______. [2026]

Smart Achievers · Accepted Answer

(3)

$Weight of wire = W$

$Cross section Area = A$

$Tension = Total weight Below Point P$

$Weight per unit length = \frac{w}{ℓ}$

$A$

$w' = \frac{w}{ℓ} \cdot \frac{2 ℓ}{3} = \frac{2 w}{3}$

$Total tension = T = W + \frac{2 w}{3}$

$Stress = \frac{T}{A}$

$Stress = \frac{W}{A} + \frac{2 W}{3 A}$

$By comparing γ = 3$

Solution

Q.
A uniform wire of length $l$ of weight $w$ is suspended from the roof with a weight of $W$ at the other end. The stress in the wire at $\frac{l}{3}$ distance from the top is $(\frac{W}{A} + \frac{2 w}{γ A}),$ where $A$ is the cross-sectional area of the wire. The value of $γ$ is ______. [2026]

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Solution

Q. A uniform wire of length l of weight w is suspended from the roof with a weight of W at the other end. The stress in the wire at l3 distance from the top is (WA+2wγA),where A is the cross-sectional area of the wire. The value of γ is ______. [2026]

Ans. (3) Weight of wire=W Cross section Area=A Tension=Total weight Below Point P Weight per unit length=wℓ Weight of wire Below point P, w'=wℓ·2ℓ3=2w3 Total tension=T=W+2w3 Stress=TA Stress=WA+2W3A By comparing γ=3

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Q.
A uniform wire of length $l$ of weight $w$ is suspended from the roof with a weight of $W$ at the other end. The stress in the wire at $\frac{l}{3}$ distance from the top is $(\frac{W}{A} + \frac{2 w}{γ A}),$ where $A$ is the cross-sectional area of the wire. The value of $γ$ is ______. [2026]