Question

A force \(F\) of same magnitude is applied tangentially on upper and lower face of a cube, in opposite directions. Side of the cube is \(L\). The upper face of the cube shifts parallel to itself by a distance \(x_1\). If another cube of same material but side \(2L\) is subjected to the above condition, then the displacement of the top layer is

• A. \( \dfrac{x_1}{6} \)
• B. \( \dfrac{x_1}{2} \)
• C. \( \dfrac{x_1}{8} \)
• D. \( \dfrac{x_1}{4} \)

Hint:

For the same material and applied force, shear strain remains constant. Displacement is directly proportional to height.

Answer 1

The Correct Option is B

Step 1: Relation of shear deformation.
Shear strain is given by \[ \text{Shear strain} = \frac{\text{displacement}}{\text{height}}. \] For the first cube, \[ \text{Shear strain} = \frac{x_1}{L}. \]
Step 2: Effect of doubling the side.
For the second cube, height becomes \(2L\). Since the force and material are the same, shear stress and hence shear strain remain the same.
Step 3: Calculating new displacement.
\[ \frac{x_2}{2L} = \frac{x_1}{L} \Rightarrow x_2 = \frac{x_1}{2}. \]
Step 4: Conclusion.
The displacement of the top layer becomes \( \dfrac{x_1}{2} \).