Question 432: Thermodynamics & KTG

Question

A steel rail of length 5 m and area of cross section 40cm
2
is prevented from expanding along its length while the temperature rises
by 10
o
C. If coefficient of linear expansion and Young’s modulus of steel are 1.2×10
−5
K
−1
and 2×10
11
Nm
−2
respectively, the force developed in the rail is approximately :

Accepted Answer

Young's modulus (Y) = $${{{F \over A}} \over {{{\Delta L} \over L}}}$$
as  $${{{\Delta L} \over L}}$$ = $$\alpha $$ $$\Delta $$$$	heta $$
$$	herefore\,\,\,$$ Y = $${{F \over {A\alpha \Delta 	heta }}}$$
$$ \Rightarrow $$$$\,\,\,$$ F = YA$$\alpha $$$$\Delta $$$$	heta $$
= 2 $$ 	imes $$ 10
11
$$ 	imes $$ 40$$ 	imes $$10
$$-$$4
$$ 	imes $$ 1.2 $$ 	imes $$ 10
$$-$$5
$$ 	imes $$ 10
= 9.6 $$ 	imes $$ 10
4
N
$$ \simeq $$ 1 $$ 	imes $$ 10
5
N

Answer

2 $$ 	imes $$ 10
7
N

Answer

1  $$ 	imes $$ 10
5
N

Answer

2 $$ 	imes $$ 10
9
N

Answer

3  $$ 	imes $$ 10
$$-$$5
N

Thermodynamics & KTG

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