A metal specimen 75 mm long was subjected to a tensile force of 10 kN . The longitudinal strain in the direction of the applied force is 0.1 . If the width of the specimen is 25 mm , what is the amount of contraction in the lateral direction? Poisson ratio = 0.3 (A) 0.75 mm (B) 2.5 mm (C) 8.75 mm (D) 7.5 mm

To find the amount of contraction in the lateral direction, we can use Poisson's ratio formula, which relates the longitudinal strain to lateral strain. The formula is given by: \[ \text{Lateral Strain} = -\text{Poisson's Ratio} \times \text{Longitudinal Strain} \] Given the longitudinal strain of 0.1 and Poisson's ratio of 0.3: \[ \text{Lateral Strain} = -0.3 \times 0.1 = -0.03 \] The original width of the specimen is 25 mm, so the amount of lateral contraction can be calculated as: \[ \text{Contraction in Lateral Direction} = \text{Original Width} \times \text{Lateral Strain} = 25 \, \text{mm} \times (-0.03) = -0.75 \, \text{mm} \] Since we're looking for the absolute value of the contraction, the answer is: **(A) 0.75 mm**. Think of Poisson's ratio as the “squeeze factor” in materials; when you stretch something long, it squishes sideways! Nice to know your materials have these quirky little characteristics, right? Understanding real-world applications of tensile testing is vital! Engineers, for instance, need this information to ensure materials behave predictably under stress—be it in skyscrapers, bridges, or even everyday objects like cars. If they didn't account for material deformation, things could get a little... shaky!