First slide

Stress and strain

Question

Two parallel and opposite forces each 5000 N are applied tangentially to the upper and lower faces of a cubical metal block of side 25 cm. The angle of shear is (The shear modulus of the metal is 80 GPa)

Moderate

A

$10^{- 4} rad$
B

$10^{- 5} rad$
C

$10^{- 6} rad$
D

$10^{- 7} rad$

Solution

Here, F = 5000 N
L = 25 cm = 25 $\times 10^{- 2} m$
A = ${(25 \times 10^{- 2} m)}^{2}$ = 625 $\times 10^{- 4} m^{2}$
$η = 80 GPa = 80 \times 10^{9} Pa$
Angle of shear, $θ = \frac{F}{Aη} = \frac{5000}{625 \times 10^{- 4} \times 80 \times 10^{9}}$
= $10^{- 6} rad$

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