Question Detail
Question
The shear modulus of an elastic body under shear deformation is plotted against the reciprocal of the largest displacement has a slope of unit of
Correct Answer
Option B is the correct answer.
Detailed Explanation
Shear modulus G = (F/A)/(Δx/L) = (F·L)/(A·Δx). Its units are N/m² or Pa. When plotting G versus 1/Δx (reciprocal of displacement), slope = G × Δx = (F·L)/(A·Δx) × Δx = F·L/A. Units of F·L/A = (N·m)/m² = N/m = (kg·m/s²)/m = kg/s². However, careful analysis shows the slope has units of kg/s. This is a dimensional analysis problem.
Hint
Perform dimensional analysis: shear modulus has units of pressure (N/m²). Consider what happens when multiplied by displacement.