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 =2×1011N/m2]
A
Normal stress is 25√3N/m2
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B
Shear stress is 25N/m2
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C
Longitudinal strain is 12.5√3×10−11
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D
Magnitude of lateral strain is 10√3×10−11
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Solution
The correct option is D Magnitude of lateral strain is 10√3×10−11 Given,
Poisson's ratio i.e ν=0.8
Young's modulus =2×1011N/m2
According to question
Normal stress=Normal forceArea
Normal force is 25√3N acting peprendicular to the surface of the cube. ⇒σN=25√31=25√3N/m2...(1) Shear stress=Shear forceArea
Similarly, 25N is the shear force, acting parallel to the surface of cube. ⇒σS=251=25N/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=25√32×1011 ⇒εN=12.5√3×10−11
εN is the strain along normal direction, also known as longitudinal strain.
Poisson ratio is defined as, ν=−Lateral strainLongitudinal strain ⇒0.8=−εS12.5√3×10−11 ⇒εS=−10√3×10−11
Hence, magnitude of lateral strain is 10√3×10−11