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 $=25GPa,g=10m{s}^{-2}$)

• 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 $4\times {10}^{-7}m$

Here, $F=\left(100kg\right)\left(10m{s}^{-2}\right)=1000N;A=(10cm\times 10cm)=100{cm}^2=100\times {10}^{-4}{m}^2$
$\eta =25GPa=25\times {10}^{9}Pa=25\times {10}^{9}N{m}^{-2};L=10cm=10\times {10}^{-2}m$

Shear modulus, $\eta =\frac{F/A}{\Delta L/L}\therefore \Delta L=\frac{FL}{\eta A}$

Substituting the given values, we get
$\Delta L=\frac{\left(1000N\right)(10\times {10}^{-2}m)}{(25\times {10}^{9}N{m}^{-2})(100\times {10}^{-4}{m}^2)}=4\times {10}^{-7}m$