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Question

For the cube of given dimensions which is fixed at the bottom and acted upon by the force as shown in figure, identify the correct statement(s).
[Poisson's ratio =0.8 and Young's modulus =2×1011 N/m2]


A
Normal stress is 253 N/m2
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B
Shear stress is 25 N/m2
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C
Longitudinal strain is 12.53×1011
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D
Magnitude of lateral strain is 103×1011
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Solution

The correct option is D Magnitude of lateral strain is 103×1011
Given,
Poisson's ratio i.e ν=0.8
Young's modulus =2×1011 N/m2
According to question


Normal stress=Normal forceArea

Normal force is 253 N acting peprendicular to the surface of the cube.
σN=2531=253 N/m2 ...(1)
Shear stress=Shear forceArea
Similarly, 25 N is the shear force, acting parallel to the surface of cube.
σS=251=25 N/m2 ...(2)
Young's modulus has been defined as ratio of stress and strain for the normal direction, at the cross-sectional area where force is acting.
Y=σNεN
εN=2532×1011
εN=12.53×1011

εN is the strain along normal direction, also known as longitudinal strain.

Poisson ratio is defined as,
ν=Lateral strainLongitudinal strain
0.8=εS12.53×1011
εS=103×1011
Hence, magnitude of lateral strain is 103×1011

(a), (b), (c), (d) are correct choices.

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