A steel wire of length (20 ~cm ) and area of crosssection (1 ~mm ^2 ) is tied rigidly at both the ends. When the temperature of the wire is changed from (40^ C ) to (20^ C ), find the change in its tension. Given, the coefficient of linear expansion for steel is (1.1 10⁻⁵ ^ C ⁻¹ ) and Young's modulus of steel is (2.0 10¹¹ Nm ⁻² ).

Step-by-step solution

Given, Young's modulus of steel wire, (Y=2 10¹¹ Nm ⁻² ) Length of wire, (l=20 ~cm =0.2 ~m ) Area of cross-section, (A=1 ~mm ^2=10⁻⁶ ~m ^2 ) Change in temperature of wire, ( aligned t & =(40-20)^ C & =20^ C & =1.1 10⁻⁵ ^ C ⁻¹ aligned ) ( ) Change in tension in the steel wire, ( aligned T & =Y A t & =2 10¹¹ 10⁻⁶ 1.1 10⁻⁵ 20 & =44 ~N aligned )