Question

a cube of aluminium of each side 4 cm is subjected to a tangential force the top face of the cube is shared through 0.012 with respect to the top face find

1) shearing strain
2) shearing stress
3) sharing force
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Answer 1

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$Here\:l = 4 cm ,delta\:l = 0.012 cm,$

$n = 2.08×10^11 dyne\:cm^-2$

$1) Shearing\:strain,$

$θ = Δl/l = 0.012/4 = <strong>0.00</strong><strong>0</strong><strong>3</strong><strong> </strong><strong>rad</strong><strong> </strong>$

$2) Area\:of\:top\:face,$

$= l^2 = (4 cm )^2 = 16 cm^2$

$Modulus\:of\:rigidity, n= shearing \:stress/shearing\: strain$

$∴ Shearing\: stress$

$= n× shearing\: strain$

$= 2.08×10^11×0.0003= <strong>6.24</strong><strong>×</strong><strong>1</strong><strong>0</strong><strong>^</strong><strong>8</strong><strong> </strong><strong>\</strong><strong>:</strong><strong>dyne</strong>\<strong>:</strong><strong>cm</strong><strong>^</strong><strong>-2</strong><strong> </strong>$

Answer 2

$Here l = 4 cm ,  Δ l = 0.012 cm,$

$n = 2.08×10^11 dyne cm^-2$

$1) Shearing strain,$

$θ = Δl/l = 0.012/4 = <strong>0.00</strong><strong>0</strong><strong>3</strong><strong> </strong><strong>rad</strong><strong> </strong>$

$2) Area of top face,$

$= l^2 = (4 cm )^2 = 16 cm^2$

$Modulus of rigidity, n= shearing stress/shearing strain$

$∴ Shearing stress$

$= n× shearing strain$

[tex] = 2.08×10^11×0.0003= 6.24×10^8 dyne cm^-2