The value of tension in a long thin metal wire has been changed from T1 to T2. The lengths of the metal wire at two different values of tension T1 and T2 are l1 and l2 respectively. The actual length of the metal wire is :

T_1l_2 - T_2l_1 \over T_1 - T_2

T_1l_1 - T_2l_2 \over T_1 - T_2

Properties of Matter PYQ — JEE Main 2021 · 20 Jul · Shift 1 · Q63 with Solution

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Correct answer: C

For a wire under tension $T$ , the extension is

$\Delta l = \frac{T L}{A Y}$

where:

So the observed length under tension $T$ is

$l = L + \frac{T L}{A Y} = L\left(1 + \frac{T}{A Y}\right)$

Let

$k = \frac{1}{A Y}$

Then

$l = L(1+kT)$

At tension $T_1$ , length is $l_1$ :

$l_1 = L(1+kT_1)$

At tension $T_2$ , length is $l_2$ :

$l_2 = L(1+kT_2)$

Multiply the first equation by $T_2$ :

$T_2 l_1 = L(T_2 + kT_1T_2)$

Multiply the second equation by $T_1$ :

$T_1 l_2 = L(T_1 + kT_1T_2)$

Now subtract:

$T_1 l_2 - T_2 l_1 = L(T_1 - T_2)$

Hence,

$L = \frac{T_1 l_2 - T_2 l_1}{T_1 - T_2}$

This corresponds to:

$\boxed{\frac{T_1 l_2 - T_2 l_1}{T_1 - T_2}}$

So the correct option is C.

Stored correct answer: C

Our derived answer: C

They match.