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Q.

The value of tension in a long thin metal wire has been changed from T₁ and 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

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a

$\frac{l_{1} + l_{2}}{2}$

b

$\frac{T_{1} l_{2} - T_{2} l_{1}}{T_{1} - T_{2}}$

c

$\frac{T_{1} l_{1} - T_{2} l_{2}}{T_{1} - T_{2}}$

d

$\sqrt{T_{1} T_{2} l_{2} l_{2}}$

answer is B.

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Detailed Solution

detailed_solution_thumbnail

We know that,

$Y = \frac{F L}{A ∆ L}$

from the question,

$Y = \frac{T_{1} l_{0}}{A (l_{1} - l_{0})} = \frac{T_{2} l_{0}}{A (l_{2} - l_{0})} 1 = \frac{T_{1} (l_{2} - l_{0})}{T_{2} (l_{1} - l_{0})} T_{2} l_{1} - T_{2} l_{0} = T_{1} l_{2} - T_{1} l_{0} (T_{1} - T_{2}) l_{0} = T_{1} l_{2} - T_{2} l_{1} l_{0} = (\frac{T_{1} l_{2} - T_{2} l_{1}}{T_{1} - T_{2}})$

Hence the correct answer is $(\frac{T_{1} l_{2} - T_{2} l_{1}}{T_{1} - T_{2}}) .$

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