Question 128: Properties of Matter

Question

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 :

Accepted Answer

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

Answer

$${{{T_1}{l_1} - {T_2}{l_2}} \over {{T_2} - {T_1}}}$$

Answer

$${{{l_1} + {l_2}} \over 2}$$

Answer

$${{{T_2}{l_1} + {T_1}{l_2}} \over {{T_1} + {T_2}}}$$

Answer

$${{{T_2}{l_1} - {T_1}{l_2}} \over {{T_2} - {T_1}}}$$

Properties of Matter

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 :

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