Two rods X and Y of different metals have lengths l_1and l_2at a certain temperature. If l_1 - l_2 =4 cm at all temperatures and coefficients of linear expansion of X and Y are 1.5 xx 10^(-5) ""^@C and 2.0 xx 10^(-5) ""^@C^(-1)respectively, then

Two rods X and Y of different metals have lengths l_1and l_2at a certa

1.	Two rods X and Y of different metals have lengths l_1and l_2at a certain temperature. If l_1 - l_2 =4 cm at all temperatures and coefficients of linear expansion of X and Y are 1.5 xx 10^(-5) ""^@C and 2.0 xx 10^(-5) ""^@C^(-1)respectively, then
Answer» `l_1=14 cm ` `l_1 = 16 cm ` `l_2 = 10cm ` `l_2 = 12 cm ` SOLUTION :INCREASE in the LENGTH of the rods when heatedby `Delta T^@C` is `Delta l_1 = l_1 alpha_1 Delta T` ` Delta l_2 = l_2 alpha_2 Delta T` Given`l_1 - l_2 = 4 cm ` at all T if `Delta l_1 = Delta l_2 ` , then `l_1 alpha_1 Delta T = l_2 alpha_2 Delta T` ` rArr l_1/l_2 = alpha_2/alpha_1 = (2.0 xx 10^(-5) )/(1.5 xx 10^(-5) ) = 4/3 ` ` rArr l_1 - l_2 = 4 cm ` `4/3 l_2 - l_2 = 4 cm ` `l_2 = 12 cm ` `l_1= 4/3 xx 12 = 16 cm `