A copper wire of length 2.2 m and a steel wire of length 1.6m, both of diameter 3mm are connected end to end. When stretched by a load, the net elongation is found to be 0.70 mm. Obtain the load applied.
`(Y_(s)=2.0xx10^(11)Nm^(-2))`
`(Y_(c)=1.1xx10^(11)Nm^(-2))`

Options

A. `1.8xx10^(2)N`
B. `1.2xx10^(2)N`
C. `3.2xx10^(4)N`
D. `2.4xx10^(2)N`

Answer

A

Explanation

Both copper and steel wires are under the same tensile stress, as the tension and area of cross-section of the wires are same.
`rArr" "(W)/(A)=Y_(c)xx((DeltaL_c)/(L_c))=Y_(s)xx((DeltaL_s)/(L_s))`
`rArr" "(DeltaL_c)/(DeltaL_s)=((Y_s)/(Y_c))xx((L_c)/(L_s))`
`=((2xx10^(11)Nm^(-2))/(1.1xx10^(11)Nm^(-2)))((2.2m)/(1.6m))`
`=2.5`
Also, `DeltaL_(c)+DeltaL_(s)=7xx10^(-4)m`
`rArr" "DeltaL_(c)=5xx10^(-4)m`
`therefore" "W=(AxxY_(c)xxDeltaL_c)/(L_c)`
`=(pi(1.5xx10^(-3)m)^(2)xx(1.1xx10^(11)Nm^(-2)xx5xx10^(-4)m))/(2.2m)`
`=1.8xx10^(2)N`