Question

The edges of an aluminmum cube are $10cm$ 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. Shear modulus of aluminium is $25\times {10}^{9}Pa$, the vertical deflection in the face to which mass is attached is

• A. $4\times {10}^{-4}m$
• B. $4\times {10}^{-7}m$
• C. $25\times {10}^{-6}m$
• D. $6\times {10}^{-7}m$

Answer 1

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

The situation as is shown in the figure. A force of 100g acts on farther face of cube as shown, due to which shear will develop.
$\eta =\frac{F/A}{x/l}$
$x=\frac{Fl}{A\eta }=\frac{100\times l}{l^2\times 25\times {10}^9}$
$x=4\times {10}^{-7}m$