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8.Mechanical Properties of Solids
easy
The edge of an aluminium cube is $10\; cm$ long. One face of the cube is firmly fixed to a vertical wall. A mass of $100 \;kg$ is then attached to the opposite face of the cube. The shear modulus of aluminium is $25\; GPa$. What is the vertical deflection of this face?
A
$7.56 \times 10^{-8} \;m$
B
$2.23 \times 10^{-6} \;m$
C
$3.92 \times 10^{-7} \;m$
D
$5.56 \times 10^{-5} \;m$
Solution
Shear modulus, $\eta=\frac{\text { Shear stress }}{\text { Shear strain }}=\frac{\frac{F}{A}}{\frac{L}{\Delta L}}$
$\therefore \Delta L=\frac{F L}{A \eta}$
$=\frac{980 \times 0.1}{10^{-2} \times\left(25 \times 10^{9}\right)}$
$=3.92 \times 10^{-7} m$
The vertical deflection of this face of the cube is $3.92 \times 10^{-7} \;m$
Standard 11
Physics
