Answer:
0.44
Explanation:
Poisson's ratio is:
ν = (3K − E) / 6K
where K is the bulk modulus and E is Young's 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 = (20 kg × 9.8 m/s²) (1.7 m) / (π (0.02 m)² × 0.0005 m)
E = 0.530×10⁹ Pa
Bulk modulus is:
K = -ΔP / (ΔV/V)
where ΔP is the change in pressure, ΔV is the change in volume, and V is the initial volume.
K = -(180 atm × 101325 Pa/atm) / (-0.012)
K = 1.52×10⁹ Pa
Therefore, the Poisson's ratio is:
ν = (3(1.52×10⁹ Pa) − 0.530×10⁹ Pa) / 6(1.52×10⁹ Pa)
ν = (3(1.52) − 0.530) / 6(1.52)
ν = 0.442
Rounded to 2 significant figures, the Poisson's ratio is 0.44.
