Solution to Exercise

1. Since the temperatures are equal,

R 1 / R 2 = ( L 1 / L 2 ) 1 / 2 = ( 100 ) 1 / 2 = 10

2. Since L 1 / L 2 = 1, we have that ( R 1 / R 2 ) 2 = ( T 2 / T 1 ) 4. Thus, taking the square root of both sides of this equation,

R 1 / R 2 = ( T 2 / T 1 ) 2 = ( 5000 / 10000 ) 2 = 1 / 4

Since the ratio of the radii scales as the square of the temperature, differences in temperature imply much larger differences in radii.