Two uniform wires of length 3m and 4m respectively are made of the same material To stretch both these wires by the same length, 0.03J and 0.05 J of work on necessary. Calculate the ratio of the cross sectional area of the two wires.

Explanation

Let the work done in the case of the first and the second wires respectively be ,
`W_1=1/2(Yal^2)/(L_1)andW_2=1/2(Ya_2l^2)/L_2`
`thereforeW_1/W_2=(alpha_1L_2)/(alpha_2L_1)or,alpha_1/alpha_2=(W_1L_1)/(W_2L_2)`
Here, `W_1=0.03J,W_2=0.05 J, L_1=3m and L_2=4 m `
`thereforealpha_1/alpha_2=(0.03times3)/(0.05times4) or,a_1:a_2=9:20`