Question

The edge of an aluminium cube is $10cm$ long. One face of the cube is firmly fixed to a vertical wall. A mass of $100kg$ is then attached to the opposite face of the cube. The vertical deflection of this face is
(Shear modulus of aluminium $=25GPa,g=10{ms}^{-2}$ )

• A. $4\times {10}^{-5}m$
• B. $4\times {10}^{-6}m$
• C. $4\times {10}^{-7}m$
• D. $4\times {10}^{-8}m$

Answer 1

The correct option is C $4\times {10}^{-7}m$

$\begin{array}{c}\text{Given,}\\ \text{. edge of cube}=10cm\\ \text{- shear modulus}=25\times {10}^{9}Pa\\ g=10m/s^2\end{array}$

$\begin{array}{cc}\mathrm{shear\; modulus}\left(\eta \right)& =\frac{\left(\frac{F}{A}\right)}{\tan \theta }\\ since\theta \text{is small}& \\ & \tan \theta =\frac{x}{L}\\ \eta & =\frac{FL}{Ax}\\ x& =\frac{FL}{An}\end{array}$

$\begin{array}{c}\text{Putting know value,}\\ x=\frac{100\times 10\times 10\times {10}^{-2}}{(10\times 10)\times {10}^{-4}\times 25\times {10}^9}\end{array}$

$x=4\times {10}^{-7}m$