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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

The length of a metal wire is l _ 1 when the tension in it is T _ 1...

The length of a metal wire is

{l}_{1}

when the tension in it is

{T}_{1}

and is

{l}_{2}

when the tension is

{T}_{2}

. The natural length of wire is

Options

A $\dfrac{{l}_{1} + {l}_{2}}{2}$
B $\sqrt{{l}_{1}{l}_{2}}$
C $\dfrac{{l}_{1}{T}_{2} - {l}_{2}{T}_{1}}{{T}_{2} - {T}_{1}}$
D $\dfrac{{l}_{1}{T}_{2} + {l}_{2}{T}_{1}}{{T}_{2} + {T}_{1}}$

Correct answer

C. $\dfrac{{l}_{1}{T}_{2} - {l}_{2}{T}_{1}}{{T}_{2} - {T}_{1}}$

Step-by-step solution

Let the original length be

l

.

In first case,

{l}_{1} = l + d{l}_{1}

Using Hooke's law,

x = \dfrac{T}{K}

Where,

x

is the displacement.

We have,

{l}_{1} = l + \dfrac{{T}_{1}}{K}

... (i)

Similarly,

{l}_{2} = l + \dfrac{{T}_{2}}{K}

... (ii)

Solving Equations. (i) and (ii), we get

l = \dfrac{{l}_{1}{T}_{2} - {l}_{2}{T}_{1}}{{T}_{2} - {T}_{1}}

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