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Question

A metal cube of side length 8.0cm has its upper surface displaced with respect to the bottom by 0.10mm when a tangential force of 4 x 109 N is applied at the top with bottom surface fixed. The rigidity modulus of the material of the cube is :

A
4×109N/m2
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B
5×1014N/m2
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C
8×109N/m2
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D
1×109N/m2
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Solution

The correct option is B 5×1014N/m2
Given,

Side length, L=8cm

ΔL=0.1mm

Force, F=4×109N

Shearing strain =0.018

Stress =4×1098×8×104N/m2

Rigidity Modulus, y=FAΔXX=4×1099×8×1040.018

y=12×1014N/m2

=5×1014N/m2

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