"The length of metallic wire is l1 when tension in it is T1. It is l2 when the tension is T2. The original length of the wire will be :"

"Assuming Hooke's law to be valid. $T \\propto (\\Delta l)$ $T = k(\\Delta l)$ Let, l 0 = natural length (original length) $\\Rightarrow T = k(l - {l_0})$ so, ${T_1} = k({l_1} - {l_0})$ & ${T_2} = k({l_2} - {l_0})$ $\\Rightarrow {{{T_1}} \\over {{T_2}}} = {{{l_1} - {l_0}} \\over {{l_2} - {l_0}}}$ $\\Rightarrow {l_0} = {{{T_2}{l_1} - {T_1}{l_2}} \\over {{T_2} - {T_1}}}$"

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

The length of metallic wire is l₁ when tension in it is T₁. It is l₂ when the tension is T₂. The original length of the wire will be :

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

Solution

Assuming Hooke's law to be valid. $T \propto (\Delta l)$ $T = k(\Delta l)$ Let, l0 = natural length (original length) $\Rightarrow T = k(l - {l_0})$ so, ${T_1} = k({l_1} - {l_0})$ & ${T_2} = k({l_2} - {l_0})$ $\Rightarrow {{{T_1}} \over {{T_2}}} = {{{l_1} - {l_0}} \over {{l_2} - {l_0}}}$ $\Rightarrow {l_0} = {{{T_2}{l_1} - {T_1}{l_2}} \over {{T_2} - {T_1}}}$

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

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The length of metallic wire is l1 when tension in it is T1. It is l2 when the tension is T2. The original length of the wire will be :

Solution

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The length of metallic wire is l₁ when tension in it is T₁. It is l₂ when the tension is T₂. The original length of the wire will be :