Two bars are given in has a length La, and coefficient of thermal expansion αa= 14/10^6°C-^-1 Bar B has a length L, and coefficient of thermal expansion αb= 16/10^6 °C^-1. The gap between two parts is k. What minimum increase in th

Before apply GATE 2021 exam and UPSC ESE 2021 and UPES CSE  2021 exam  prepration. This question of strength of material subject is important .In this question Thermal stress and strain formula need to be apply.

Two bars  A has a length La, and coefficient of thermal expansion αa= 14/10^6°C-^-1 Bar B has a length L, and coefficient of thermal expansion αb= 16/10^6 °C^-1. The gap between two parts is k. What minimum increase in the temperature (At) of the bars above their initial temperature 0 is necessary to cause them to come into contact. (La=1.5m, Lb=2.4m,k=0.7mm)


for GATE exam and UPSC ESE exam point of view this question of strength of material subject is important .In this question Thermal stress and strain formula need to be apply.

SOLUTION :- 

Given,

αa= 14/10^6 °C^-1

αb= 64/10^6 °C^-1

La=1.5m,

Lb=2.4m

k=0.7mm = 0.0007 m

Sum of change in length of Bar A and B due to change in the temprature will be equal to the "K"

So, ΔLa + ΔLb = K

αa×ΔT×La + αb×ΔT×Lb = K

(14/10^6)×ΔT×1.5 + (16/10^6)×ΔT×2.4 = 0.0007

so, ΔT = 11.78 °C

now, we know that

ΔT = T2 - T1

11.78 = T2 - 0

T2 = 11.78 °C

Hence, the minimum increase in the temperature of the bars above their initial temperature 0 is necessary to cause them to come into contact is 11.78 °C