Question

Match the following mechanical properties with the corresponding formula. \[ \begin{array}{|c|l|c|l|} \hline \textbf{Property} & & \textbf{Formula} & \\ \hline P & \text{Modulus of Elasticity} & I & C+\sigma_n\tan\phi \\ Q & \text{Compressive Strength} & II & \dfrac{\text{Lateral Strain}}{\text{Longitudinal Strain}} \\ R & \text{Shear Strength} & III & \dfrac{\text{Stress}}{\text{Strain}} \\ S & \text{Poisson's Ratio} & IV & \dfrac{\text{Normal Force}}{\text{Area}} \\ \hline \end{array} \]

• A. \(P\!-\!I,\;Q\!-\!II,\;R\!-\!III,\;S\!-\!IV\)
• B. \(P\!-\!I,\;Q\!-\!IV,\;R\!-\!III,\;S\!-\!II\)
• C. \(P\!-\!III,\;Q\!-\!IV,\;R\!-\!I,\;S\!-\!II\)
• D. \(P\!-\!III,\;Q\!-\!II,\;R\!-\!I,\;S\!-\!IV\)

Hint:

Remember the basic relations: \[ \boxed{ \begin{aligned} E&=\frac{\text{Stress}}{\text{Strain}}, \mu&=\frac{\text{Lateral Strain}}{\text{Longitudinal Strain}}, \sigma&=\frac{P}{A}, \tau&=c+\sigma_n\tan\phi. \end{aligned} } \]

Answer 1

The Correct Option is C

Step 1: Match each property with its standard formula. \[ \begin{aligned} \text{Modulus of Elasticity} &= \frac{\text{Stress}}{\text{Strain}} &&\Rightarrow P-III,[2mm] \text{Compressive Strength} &= \frac{\text{Normal Force}}{\text{Area}} &&\Rightarrow Q-IV,[2mm] \text{Shear Strength} &= C+\sigma_n\tan\phi &&\Rightarrow R-I,[2mm] \text{Poisson's Ratio} &= \frac{\text{Lateral Strain}} {\text{Longitudinal Strain}} &&\Rightarrow S-II. \end{aligned} \]

Step 2: Choose the correct matching. Hence, \[ \boxed{ P-III,\; Q-IV,\; R-I,\; S-II } \] Therefore, \[ \boxed{(C)} \] is the correct answer.