Question 307: Properties of Matter

Question

A steel rod with y = 2.0 $$	imes$$ 10
11
Nm
$$-$$2
and $$\alpha$$ = 10
$$-$$5
$$^\circ$$C
$$-$$1
of length 4 m and area of cross-section 10 cm
2
is heated from 0$$^\circ$$C to 400$$^\circ$$C without being allowed to extend. The tension produced in the rod is x $$	imes$$ 10
5
N where the value of x is ____________.

Accepted Answer

Given, the Young's modulus of the steel rod, Y = 2 $$	imes$$ 10
11
Pa
Thermal coefficient of the steel rod, $$\alpha$$ = 10
$$-$$5
$$^\circ$$C
The length of the steel rod, l = 4 m
The area of the cross-section, A = 10 cm
2
The temperature difference, $$\Delta$$T = 400$$^\circ$$C
As we know that,
Thermal strain = $$\alpha$$ $$\Delta$$T
Using the Hooke's law
Young's modulus (Y) = $${{Thermal\,stress} \over {Thermal\,strain}} = {{F/A} \over {\alpha \,\Delta \,T}}$$
Thermal stress, $$F = YA\,\alpha \,\Delta \,T$$
Substitute the values in the above equation, we get
$$F = 2 	imes {10^{11}} 	imes 10 	imes {10^{ - 4}} 	imes {10^{ - 5}} 	imes (400)$$
$$ = 8 	imes {10^5}N$$
Comparing with, $$F = x 	imes {10^5}N$$
The value of the x = 8.

Properties of Matter

A steel rod with y = 2.0 $\times 10 11 Nm -2 and \alpha = 10 -5 ^\circC -1 of length 4 m and area of cross-section 10 cm 2 is heated from 0^\circC to 400^\circC without being allowed to extend. The tension produced in the rod is x \times$ 10 5 N where the value of x is ____________.

Integer / Numeric Answer Type