What force must be applied to each end of the rod to prevent it from contracting when it is cooled from 120 ∘c to 10 ∘c?

Linear thermal expansion coef brass 19e-6 / K

∆L = αL∆T = (19e-6) (1.85) (110) = 0.00387 meter or 3.87 mm

Second part involves linear elasticity.

for brass, young's modulus is 15e6 psi or 100 GPa

cross-sectional area of rod is π (0.008) ² = 0.0002 m²

F = EA∆L/L

F = (100e9) (0.0002) (0.00387) / (1.85)

F = 42000 or 42 kN