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NTA Abhyas 2020

Exam: NTA Abhyas
Year: 2020
Subject: Physics
Chapter: Mechanical Properties of Solids

NTA Abhyas 2020 · Physics · Mechanical Properties of Solids

There is no change in the volume of a wire due to the change in its...

There is no change in the volume of a wire due to the change in its length on stretching. The Poisson's ratio of the material of the wire is

Options

A $+ \dfrac{1}{2}$
B $- \dfrac{1}{2}$
C $+ \dfrac{1}{4}$
D $- \dfrac{1}{4}$

Correct answer

B. $- \dfrac{1}{2}$

Step-by-step solution

Volume of cylindrical wire,

V = \dfrac{{\pir}^{2}L}{4}

, where

x

is the diameter of wire.Differentiating both sides,

\dfrac{dV}{dx} = \dfrac{\pi}{4} \left[2xL + x^{2} ⋅ \dfrac{dL}{dx}\right]Also, volume remains constant

∴

\dfrac{dV}{dx} =0 ∴ 2xL + x^{2}\dfrac{dL}{dx} =0 ⟹ 2xL = - x^{2}\dfrac{dL}{dx}

⟹

\dfrac{dxx}{dLL} = - \dfrac{1}{2}Poisson's ratio

= -

\dfrac{1}{2}

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