Question 1: Thermodynamics & KTG

Question

Steel wire of lenght ‘L’ at 40
o
C is suspended from the ceiling and then a mass ‘m’ is hung from its free
end. The wire is cooled down from 40
o
C to 30
o
C to regain its original length ‘L’. The coefficient of linear
thermal expansion of the steel is 10
−5
/
o
C, Young’s modulus of steel is 10
11
N/m
2
and radius of the wire is 1 mm. Assume that L >> diameter of the wire. Then the value of ‘m’ in kg is nearly

Accepted Answer

Change in length $\Delta L = L\,\alpha \,\Delta T$ ..... (i)
Also $Y = {{mgL} \over {A\Delta L}} \Rightarrow \Delta L = {{mgL} \over {YA}}$ ..... (ii)
Equation (i) and (ii) we get ($\because$ $A = \pi {r^2}$)
$m = {{\alpha \Delta TY 	imes \pi {r^2}} \over g}$
$ = {{({{10}^{ - 5}}) 	imes (10) 	imes ({{10}^{11}}) 	imes 3.14 	imes {{(1 	imes {{10}^{ - 3}})}^2}} \over {9.8}}$
= 3.2 kg $ \simeq $ 3 kg

Thermodynamics & KTG

Integer / Numeric Answer Type