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Mechanical Properties of Solids

Multiple Choice Questions

81.
The length of a metal wire is L₁ when the tension is T₁ and L₂ when the tension is T₂. The unstretched length of wire is

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

$\sqrt{L_{1} L_{2}}$

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

$\frac{T_{2} L_{1} + T_{1} L_{2}}{T_{2} + T_{1}}$

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

Let the initial length of the metal wire is L.

The strain at tension T₁ is ΔL₁ = L₁ − L

The strain at tension T₂ is ΔL₂ = L₂ − L

Suppose, the Young's modulus of the wire is Y, then

$\frac{\frac{T_{1}}{A}}{\frac{∆ L_{1}}{L}} = \frac{\frac{T_{2}}{A}}{\frac{∆ L_{2}}{L}}$

where, A is an cross-section of the wire, assume to be same at all the situations

$\Rightarrow \frac{T_{1}}{A} \times \frac{L}{∆ L_{1}} = \frac{T_{2}}{A} \times \frac{L}{∆ L_{2}} \Rightarrow \frac{T_{1}}{(L_{1} - L)} = \frac{T_{2}}{(L_{2} - L)} \Rightarrow T_{1} (L_{2} - L) = T_{2} (L_{1} - L) \Rightarrow L = \frac{T_{2} L_{1} - T_{1} L_{2}}{T_{2} - T_{1}}$

Previous Year Papers

Test Series

Test Yourself

Multiple Choice Questions

81. The length of a metal wire is L1 when the tension is T1 and L2 when the tension is T2. The unstretched length of wire is L1 + L22 L1L2 T2L1 - T1L2T2 - T1 T2L1 + T1L2T2 + T1

81.
The length of a metal wire is L₁ when the tension is T₁ and L₂ when the tension is T₂. The unstretched length of wire is

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

$\sqrt{L_{1} L_{2}}$

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

$\frac{T_{2} L_{1} + T_{1} L_{2}}{T_{2} + T_{1}}$