Thermal Expansion of Ring and Sphere · CAP 2017 #12
Physics · thermodynamics
Problem
The expansion of a rod when heated is described by the equation L(T)=L0(1+αΔT) where L0 is the length of the rod at an initial temperature and ΔT is the change in temperature, and α is a coefficient that depends on the type of material used. Now suppose we have a ring with α=10−5/°C and a sphere with α=0.5×10−5/°C. The sphere is of radius 10.005 cm, the ring has an inner radius of 10.000 cm, both when measured at 20°C. At what temperature does the sphere just fit through the ring?
a) 100°C
b) 120°C
c) 70°C
d) 360°C
e) 210°C