Test Index

Mechanical Properties of Solids

© examsnet.com
Question : 6 of 21
Marks: +1, -0
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?
Solution:  
Here, side of cube, L = 10 cm = 0.1 m
A=A= Area of the face (1)=L×L=L2=(0.1)2=0.01m2(1)=L \times L = L^{2} = (0.1)^{2} = 0.01 \text{m}^{2}
Mass attached to face (1),M=100kg(1), M=100 \text{kg}
If F be the tangential force on face (1) due to this mass, then
F=Mg=100×9.8NF=M g=100 \times 9.8 \text{N}
∴ Shear stress on the face
=FA=100×9.80.01Nm−2= \frac{F}{A}= \frac{100 \times 9.8}{0.01} \text{N} \text{m}^{-2}
Shear modulus of aluminium,
η=25GPa=25×109Nm−2\eta = 25 \text{GPa} = 25 \times 10^{9} \text{N} \text{m}^{-2}
We know that
η= Shearing stress  Shearing strain \eta = \frac{\text{ Shearing stress }}{\text{ Shearing strain }}
Let Δy\Delta y = vertical displacement of the face = ?
∴\therefore Shearing strain =ΔyL= Shearing stressη= \frac{\Delta y}{L}= \frac{\text{ Shearing stress}}{\eta}
Δy=Shearing stress η×L\Delta y = \frac{\text{Shearing stress }}{\eta} \times L
=9.8×104×0.125×109= \frac{9.8 \times 10^{4} \times 0.1}{25 \times 10^{9}}
=0.0392×10−5m=0.0392 \times 10^{-5} \text{m}
=0.0392×10−3cm=0.0392 \times 10^{-3} \text{cm}
=4×10−7m=4 \times 10^{-7} \text{m}
© examsnet.com
Go to Question: