Question

The lower edge of a square slab of side $50$cm and thickness $20$cm is rigidly fixed to the base of a table. A tangential force of $30$N is applied to the slab. If the shear moduli of the material is $4\times {10}^{10}N/m^2$, then displacement of the upper edge, in maters is?

• A. $4\times {10}^{-12}$
• B. $4\times {10}^{-10}$
• C. $6\times {10}^{-10}$
• D. $6\times {10}^{-12}$
• E. $8\times {10}^{-10}$

Answer 1

Answer: (C)

$6\times {10}^{-10}$

Shear strain, $\epsilon =\tan \theta =\theta =\frac{x}{l}$

$\eta =\frac{\sigma }{\epsilon }$

or $x=\frac{F.l}{A.\eta }$

Given $F=30$N

$A=50\times 50\times {10}^{-4}$

$\eta =4\times {10}^{10}$

$x=\frac{30\times 20\times {10}^{-2}}{50\times 50\times {10}^{-4}\times 4\times {10}^{10}}$

$=\frac{6}{2500\times 4\times {10}^{-4}\times {10}^{10}}$

$=6\times {10}^{-10}$.