Question

A metal rod having linear expansion coefficeint
2x10^-5°C has a length of 1 m at 20°C the
temperature at which it is shortened by 1 mm is
a) -20°C b) -15°C -) -30°C
d) -25°C​

Answer 1

answer : option (c) -30°C

explanation : Length of rod , L = 1m at temperature 20°C

linear expansion coefficient of metal rod, α = 2 × 10^-5/°C

we have to find temperature at which it is shortened by 1mm.

let temperature is T.

change in length , ∆l = -1mm [ negative sign indicates rod is shortened]

using formula, ∆l = Lα∆T

or, -1mm = 1m × 2 × 10^-5/°C × (T - 20°C)

or, -10^-3 m = 2 × 10^-5 (T - 20)

or, -100/2 = T - 20°

or, -50 + 20 = T

or, T = -30°C

hence, temperature = -30°C