Question 144: Properties of Matter

Question

The length of metallic wire is l
1
when tension in it is T
1
. It is l
2
when the tension is T
2
. 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 l 1 when tension in it is T 1 . It is l 2 when the tension is T 2 . The original length of the wire will be :

Choose the correct answer: