Calculate the modulus of rigidity of a metal, if a metal cube of side 40 cm is subjected to a shearing force of 2000 N.
Calculate the modulus of rigidity of a metal, if a metal cube of side 40 cm is subjected to a shearing force of 2000 N. The upper surface is displaced through 0.5 cm with respect to the bottom. Calculate the modulus of rigidity of the metal.
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Given: L = 40 cm = 0.4 m,
F = 2000 N = 2 × 103N
l = 0.5 cm = 0.005 m, A = L2 = 0.16 m2
To find: Modulus of rigidity (n)
Formulae:
i. θ = \(\frac{l}{L}\)
ii. n = \(\frac{F}{A\theta}\)
Calculation:
From formula (i),
θ = \(\frac{0.005}{0.4}\) = 0.0125
From formula (ii),
n = \(\frac{2\times10^3}{0.16\times0.0125}\) = 1 × 106 N/m2
The modulus of rigidity of the metal cube is 1 × 106 N/m2.
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