"The length of a metal wire is l1, when the tension in it is T1 and is l2 when the tension is T2. The natural length of the wire is :"

"${T_1} = k({l_1} - {l_0})$ ${T_2} = k({l_2} - {l_0})$ ${{{T_1}} \\over {{T_2}}} = {{{l_1} - {l_0}} \\over {{l_2} - {l_0}}}$ ${{{T_1}{l_2} - {T_2}{l_1}} \\over {{T_1} - {T_2}}} = {l_0}$"

Medium MCQ +4 / -1 PYQ · JEE Mains 2021

The length of a metal wire is l₁, when the tension in it is T₁ and is l₂ when the tension is T₂. The natural length of the wire is :

A $\sqrt {{l_1}{l_2}}$
B ${{{l_1}{T_2} - {l_2}{T_1}} \over {{T_2} - {T_1}}}$ Correct answer
C ${{{l_1}{T_2} + {l_2}{T_1}} \over {{T_2} + {T_1}}}$
D ${{{l_1} + {l_2}} \over 2}$

Solution

${T_1} = k({l_1} - {l_0})$ ${T_2} = k({l_2} - {l_0})$ ${{{T_1}} \over {{T_2}}} = {{{l_1} - {l_0}} \over {{l_2} - {l_0}}}$ ${{{T_1}{l_2} - {T_2}{l_1}} \over {{T_1} - {T_2}}} = {l_0}$

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Subject: Physics · Chapter: Properties of Solids and Liquids · Topic: Elasticity

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The length of a metal wire is l1, when the tension in it is T1 and is l2 when the tension is T2. The natural length of the wire is :

Solution

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The length of a metal wire is l₁, when the tension in it is T₁ and is l₂ when the tension is T₂. The natural length of the wire is :