Question

A 8 cm cube has its upper face displaced by 0.5 mm by a tangential force of 10 kN. What is the shear modulus of the cube?

विकल्प

• 2 × 10¹⁰ N/m²

• 2.5 × 10⁸ N/m²

• 1 × 10⁹ N/m²

• 1 N/m²

Answer 1

2.5 × 10⁸ N/m²

Explanation:

Side of cube = 8 cm = 8 × 10⁻² m

Force on upper face = 10 × 10³ N

Displacement = 0.5 × 10⁻³ N

Area of upper face = (8 × 10⁻²)² = 64 × 10⁻⁴ m²

Displacement = 0.5 × 10⁻³ m

∴ G = `("F" xx "L")/("A" xx Δ"L")`

= `(10^4 xx 8 xx 10^-2)/(64 xx 10^-4 xx 0.5 xx 10^-3)`

= 2.5 × 10⁸ N/m²