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?

Options

A. `2:1`
B. `3:2`
C. `4:3`
D. `5:3`

Answer

C

Explanation

For rod of metal A
` 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`