If a spherical glass marble has a radius of 0.00665 m at 1.02×105 Pa, at what pressure will it have a radius of 0.00650 m?

Question

If a spherical glass marble has a radius of 0.00665 m at 1.02×105 Pa, at what pressure will it have a radius of 0.00650 m?

Thanks

Answer 1

Young's modulus is

E = stress / strain = σ / ε =
= (F / A₀) / (∆L / L) ,
E for glass, 50 GPa = 50•10^9 Pa .
ΔL= R1-R2=0.00665-0.00650=5•10^−5 m.
p=E• ΔL/L=50•10^9•5•10^−5/0.00665=3.76•10^8 Pa