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Q.

A metal cube of side length 8.0 cm has its upper surface displaced with respect to the bottom by 0.10mm when tangential force of $4 \times 10^{4} N$ is applied at the top with bottom

surface fixed. The rigidity modulus of the material of the cube is

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a

$8 \times 10^{9} N m^{- 2}$

b

$5 \times 10^{9} N m^{- 2}$

c

$4 \times 10^{9} N m^{- 2}$

d

$108 N m^{- 2}$

answer is B.

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Detailed Solution

Rigidity modulus $η = \frac{F / A}{\tan θ}$

$\tan θ = \frac{0.10 \times 10^{- 3}}{8 \times 10^{- 2}} = \frac{1}{800}$

$η = \frac{4 \times 10^{4} \times 800}{8 \times 8 \times 10^{- 4}} = 5 \times 10^{9} N / m^{2}$

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A metal cube of side length 8.0 cm has its upper surface displaced with respect to the bottom by 0.10mm when tangential force of 4×104N is applied at the top with bottom surface fixed. The rigidity modulus of the material of the cube is