Question

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 ______.

Options

• `(T_1l_2 - T_2l_1)/(T_1 - T_2)`

• `sqrt(T_1T_2l_1l_2)`

• `(l_1 + l_2)/2`

• `(T_1l_1 - T_2l_2)/(T_1 - T_2)`

Answer 1

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 `bbunderline((T_1l_2 - T_2l_1)/(T_1 - T_2))`.

Explanation:

Using the phrase,

`T/A = "Υ"(deltal)/l`

Now, `T_1 = (k[l_1 - l])/l` ...........(i)

And, `T_2 = (k[l_2 - l])/l` ...........(ii)

On solving (i) and (ii),

`l = (T_1l_2 - T_2l_1)/(T_1 - T_2)`