A steel wire of cross section 1 mm2 is heated at 60^(@) C and tied between two ends family. Calculate change in tension when temperature becomes 30^(@) C coefficient of linear expansion for steel is alpha = 1.1 xx 10 ^(-5) "”^(@)C ^(-1), Y =2 xx 10 ^(11) Pa.(Change in length of wire due to change in temperature (Delta t) is Delta l= alpha l Delta t)

A steel wire of cross section 1 mm2 is heated at 60^(@) C and tied bet

1.	A steel wire of cross section 1 mm2 is heated at 60^(@) C and tied between two ends family. Calculate change in tension when temperature becomes 30^(@) C coefficient of linear expansion for steel is alpha = 1.1 xx 10 ^(-5) "”^(@)C ^(-1), Y =2 xx 10 ^(11) Pa.(Change in length of wire due to change in temperature (Delta t) is Delta l= alpha l Delta t)
Answer» Solution :Here `A = 1 mm ^(2) = 10 ^(-6) m ^(2)` `theta _(1) = 60 ""^(@)C, theta _(2) = 30 ""^(@) C` `therefore Delta theta = 60-30 = 30 "^(@)C` `therefore ALPHA = 1.1 xx 10 ^(-5) ""^(@)C ^(-1)` `therefore Y = 2 xx 10 ^(11) PA` here TEMPERATURE change `= Delta theta` Due to `Delta theta` change in temperature chang ein length of wire `(Delta l)/(l) = alpha xx Delta theta ` `=1.1 xx 10 ^(-5) xx 30 ^(@)` `= 3.3 xx 10 ^(-4)` Now Young.s Modulus `Y=(A )/(( Delta l )/( l ))` `therefore F = ( YA Delta l )/(l )= 2 xx 10 ^(11) xx 10 ^(-6) xx 3.3 xx 10 ^(-4)` `=6.6 xx 10 ^(1) ` `therefore F = 66 N`