Answer:
ν = 0.45
K = 2.5×10¹¹ Pa
Explanation:
Poisson's ratio is:
ν = E/(2G) − 1
where E is Young's modulus and G is the shear modulus.
Young's modulus is:
E = FL / (AΔL)
where F is the force, L is the initial length, A is the cross sectional area, and ΔL is the change in length.
E = (0.33 kg × 9.8 m/s²) (2 m) / (π (0.00016 m)² × 0.001 m)
E = 8.04×10¹⁰ Pa
Shear modulus is:
G = τL / (Jθ)
where τ is the torque, L is the length, J is the second moment of inertia, and θ is the angular deflection.
G = (1.5×10⁻⁵ Nm) (2 m) / ((π/2 (0.00016 m)⁴) (60° × π / 180°))
G = 2.78×10¹⁰ Pa
The Poisson's ratio is therefore:
ν = (8.04×10¹⁰ Pa) / (2 × 2.78×10¹⁰ Pa) − 1
ν = 0.446
And the bulk modulus is:
K = E / (3 − 6ν)
K = (8.04×10¹⁰ Pa) / (3 − 6 × 0.446)
K = 2.48×10¹¹ Pa
Rounded to 2 significant figures, the Poisson's ratio is 0.45 and the bulk modulus is 2.5×10¹¹ Pa.
