Question

A cylindrical alloy rod is subjected to a tensile force such that its length increases by \(4\%\) from its original length. During this deformation, the diameter of the rod is observed to decrease by \(1\%\). What is the Poisson's ratio of the alloy?

• A. \(0.15\)
• B. \(0.20\)
• C. \(0.25\)
• D. \(0.30\)

Hint:

Poisson's ratio is given by \[ \boxed{ \mu = -\frac{\varepsilon_{\text{lateral}}} {\varepsilon_{\text{longitudinal}}}. } \] The negative sign accounts for the reduction in lateral dimensions during tensile loading.

Answer 1

The Correct Option is C

Step 1: Recall the definition of Poisson's ratio. Poisson's ratio is \[ \boxed{ \mu = -\frac{\text{Lateral Strain}}{\text{Longitudinal Strain}}. } \]

Step 2: Calculate the strains. Longitudinal strain, \[ \varepsilon_L = \frac{\Delta L}{L} = 4\% = 0.04. \] Lateral strain, \[ \varepsilon_t = -\frac{\Delta d}{d} = -1\% = -0.01. \] Therefore, \[ \mu = -\frac{-0.01}{0.04} = 0.25. \] Hence, \[ \boxed{0.25} \] is the correct answer. Thus, \[ \boxed{(C)} \] is the correct answer.