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A rod of length 50 cm is made of metal A and elongates by 0.2 cm when it is heated from 0^@C to 100^@C . Another rod made of metal B is of length 60 cm and elongates by 0.18 cm when heated from 0^@C to 100^@C . A composite rod of length 80 cm is made by welding pieces of rods A and B, placed end to end. When metal C is heated from 0^@C to 50^@C , it gets elongated by 0.08 cm.What is the ratio of linear expansion of metal A and metal B? |
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Answer» `2:1` ` Delta L_A = alpha_A L_A Delta T` ` therefore alpha_A = (Delta L_A)/(L_A Delta T) = (0.2)/(50 XX 100) = 4 xx 10^(-5) ""^@C^(-1)` For rod of metal B `alpha_B = (Delta L_B)/(L_B Delta T) = (0.81)/(60 xx 100) = 3 xx 10^(-5) ""^@C^(-1)` ` therefore alpha_A/alpha_B = 4/3 = 4:3` |
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