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 $l_{1} a n d l_{2}$ respectively. The actual length of the metal wire is:

Option 1 -

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

Option 2 -

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

Option 3 -

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

Option 4 -

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

2 Views | Posted a month ago

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1 Answer

Answered by

alok kumar singh | Contributor-Level 10

a month ago

Correct Option - 1

Detailed Solution:

Assuming Tension in metal wire suspended from roof varies linearly and 0 and T₀ ( developed due its own weight) are tensions are ends of wire of length $l .$ So

$T_{1} α (l_{1} - l), a n d T_{2} α (l_{2} - l)$

$\frac{T_{1}}{T_{2}} = \frac{l_{1} - l}{l_{2} - l} \Rightarrow l = \frac{T_{1} l_{2} - T_{2} l_{1}}{T_{1} - T_{2}}$

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The value of tension in a long thin metal wire has been changed from T₁ to T₂. The lengths of the metal wire at two different values of tension T₁ and T₂ are $l_{1} a n d l_{2}$ respectively. The actual length of the metal wire is:

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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 l 1 a n d l 2 respectively. The actual length of the metal wire is:

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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 $l_{1} a n d l_{2}$ respectively. The actual length of the metal wire is: