16. In order to have a difference of 25 cm in their lengths at all temperature, lengths of
iron and copper rods at 0oC are
6 6 12 10 / , 18 10 / o o of iron C of copper
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answer : option (4) 60cm , 85 cm
let length of iron is x and length of copper is y
a/c to question,
x - y = 25 cm .......(1)
difference of their lengths is 25cm at all temperature.
x - y = x(1 + α_i∆T) - y(1 + α_c∆T)
⇒x - y = (x - y) + (xα_i∆T -yα_c∆T)
⇒x/y = α_c/α_i = {17 × 10^-6/°C}/{12 × 10^-6/°C}
⇒x/y = 17/12
⇒12x = 17y .........(2)
from equations (1) and (2) we get,
12x - 12y = 25 × 12
⇒17y - 12y = 25 × 12
⇒y = 60 cm and hence x = 85 cm
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