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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

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

b

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

c

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

d

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

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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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