Question 139: Properties of Matter

Question

The value of tension in a long thin metal wire has been changed from T
1
to T
2
. The lengths of the metal wire at two different values of tension T
1
and T
2
are l
1
and l
2
respectively. The actual length of the metal wire is :

Accepted Answer

Suppose, I
0
be the actual length of metal wire and Y be its Young's modulus.
From Hooke's law,
$$Y = {{T{I_0}} \over {A\Delta I}}$$
where, $$\Delta I = I - {I_0}$$
$$ \Rightarrow Y = {{T{I_0}} \over {A(I - {I_0})}}$$ or $$I - I = {{T{I_0}} \over {AY}}$$
$$	herefore$$ $${{{I_1} - {I_0}} \over {{I_2} - {I_0}}} = {{{T_1}{I_0}} \over {AY}} 	imes {{AY} \over {{T_2}{I_0}}} = {{{T_1}} \over {{T_2}}} $$
$$\Rightarrow {I_1}{T_2} - {I_0}{T_2} = {I_2}{T_1} - {I_0}{T_1}$$
$$ \Rightarrow {I_0} = {{{I_1}{T_2} - {I_2}{T_1}} \over {{T_2} - {T_1}}} = {{{T_1}{I_2} - {T_2}{I_1}} \over {({T_1} - {T_2})}}$$

Answer

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

Answer

$$\sqrt {{T_1}{T_2}{l_1}{l_2}} $$

Answer

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

Answer

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

Properties of Matter

The value of tension in a long thin metal wire has been changed from T 1 to T 2 . The lengths of the metal wire at two different values of tension T 1 and T 2 are l 1 and l 2 respectively. The actual length of the metal wire is :

Choose the correct answer: