A brass rod is 76 cm long and an aluminum rod is 43.0 cm long when both rods are
ID: 2154881 • Letter: A
Question
A brass rod is 76 cm long and an aluminum rod is 43.0 cm long when both rods are at an initial temperature of 0? C. The rods are placed in line with a gap of 1 cm 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 ? 10-5 K-1 and 2.4 ? 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:
A brass rod is 76 cm long and an aluminum rod is 43.0 cm long when both rods are at an initial temperature of 0? C. The rods are placed in line with a gap of 1 cm 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 ? 10-5 K-1 and 2.4 ? 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:Explanation / Answer
for brass rod
L=L0(1+*) where =coefficient of expansion &, = change in temperature ,L0 = initial length
increase in length,L=L-L0 = L0 =76 *(2.0 × 10^-5)*
for aluminium rod
L=L0(1+*) where =coefficient of expansion &, = change in temperature ,L0 = initial length
increase in length,L=L-L0 = L0 =43 *(2.4 × 10^-5)*
change in temperature is same for both so is same
now, increase in length of aluminium/increase in length of brass =43 *(2.4 × 10^-5)* / 76 *(2.0 × 10^-5)*
= 0.6789
so the required ratio is 0.68
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