Mechanical Properties of Solids

Question : 6

Total: 21

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= Area of the face (1)=L×L=L2=(0.1)2=0.01m2
Mass attached to face (1),M=100kg
If F be the tangential force on face (1) due to this mass, then
F=Mg=100×9.8N
∴ Shear stress on the face
=

100×9.8

0.01

N m−2
Shear modulus of aluminium,
η=25GPa=25×109N m−2
We know that
η=

Shearing stress

Shearing strain

Let Δy = vertical displacement of the face = ?
∴ Shearing strain =

Δy

Shearing stress

Δy=

Shearing stress

×L
=

9.8×104×0.1

25×109

=0.0392×10−5m
=0.0392×10−3cm
=4×10−7m

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