Question

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.

Answer 1

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.