Question

In order to have a difference of 25 cm in their lengths at all temperature,
lengths of iron and copper rods at 0 °C are ( a of iron = 12 * 10-6/°C), of
copper).
1) 85 cm, 110 cm
2) 50 cm, 25 cm
3/85 cm, 60 cm
4) 60 cm, 85 cm​

Answer 1

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

Answer 2

Answer:

$\huge\star\mathfrak\blue{{Answer:-}}$

$\huge\star\mathfrak\blue{{4) 60 cm, 85 cm}}$