JEE MAIN - Physics (2021 - 20th July Evening Shift - No. 5)
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 :
$$\sqrt {{l_1}{l_2}} $$
$${{{l_1}{T_2} - {l_2}{T_1}} \over {{T_2} - {T_1}}}$$
$${{{l_1}{T_2} + {l_2}{T_1}} \over {{T_2} + {T_1}}}$$
$${{{l_1} + {l_2}} \over 2}$$
Explanation
$${T_1} = k({l_1} - {l_0})$$
$${T_2} = k({l_2} - {l_0})$$
$${{{T_1}} \over {{T_2}}} = {{{l_1} - {l_0}} \over {{l_2} - {l_0}}}$$
$${{{T_1}{l_2} - {T_2}{l_1}} \over {{T_1} - {T_2}}} = {l_0}$$
$${T_2} = k({l_2} - {l_0})$$
$${{{T_1}} \over {{T_2}}} = {{{l_1} - {l_0}} \over {{l_2} - {l_0}}}$$
$${{{T_1}{l_2} - {T_2}{l_1}} \over {{T_1} - {T_2}}} = {l_0}$$
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