Question 187: Properties of Matter

Question

The pressure that has to be applied to the ends of a steel wire of length $$10$$ $$cm$$ to keep its length constant when its temperature is raised by $${100^ \circ }C$$ is: 
(For steel Young's modulus is $$2 	imes {10^{11}}\,\,N{m^{ - 2}}$$ and coefficient of thermal expansion is $$1.1 	imes {10^{ - 5}}\,{K^{ - 1}}$$ )

Accepted Answer

Young's modulus $$Y = {{stress} \over {strain}}$$
$$stress = Y 	imes strain$$
$$Stress$$ in steel wire $$=$$ Applied $$pressure$$
$$Pressure$$ $$=$$ $$stress$$ $$=$$ $$Y 	imes \,strain$$
$$Strain = {{\Delta L} \over L} = \alpha \Delta T$$ (As length is constant)
$$ = 2 	imes {10^{11}} 	imes 1.1 	imes {10^{ - 5}} 	imes 100$$
$$ = 2.2 	imes {10^8}Pa$$

Answer

$$2.2 	imes {10^8}\,\,Pa$$

Answer

$$2.2 	imes {10^9}\,\,Pa$$

Answer

$$2.2 	imes {10^7}\,\,Pa$$

Answer

$$2.2 	imes {10^6}\,\,Pa$$

Properties of Matter

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