A brass rod is 69.5 cm long and an aluminum rod is 49.1 cm long when both rods a

Question

A brass rod is 69.5 cm long and an aluminum rod is 49.1 cm long when both rods are at an initial temperature of 0

A brass rod is 69.5 cm long and an aluminum rod is 49.1 cm long when both rods are at an initial temperature of 0 degree C. The rods are placed in line with a gap of 1.4cm between them. The distance between the far ends of the rods is maintained at 120.0 cm throughout. The temperature is raised until the two rods are barely in contact. The coefficients of linear expansion of brass and aluminum are 2.0 Times 10-5 K-1 and 2.4 Times 10-5 K-1, respectively. In the figureb, the ratio of the increase in the length of the aluminum rod to that of the brass rod, is closest to: 1.13 0.92 0.85 1.06 .99

Explanation / Answer

Given the rods are initially at same temp , then they are raised to same temp

So chnage in length = alpha x dt x initial length

here dt is constant

So dL 1 / dL2 = alpha 1 L1 / apha 2 L2

ratio = 2.4 x 10-5 x 49.1 / 2 x 10-5 x 69.5

ratio = 0.847

ratio is 0.847

so the answer is C

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