Question

A steel wire of length 4.7 m and cross section 3 x 103 m2 stretches by the same amount as a copper wire of length 3.5 m and cross section 4 x 10-5 m2 under a given load. What is the ratio of the Young's modulus of steel to that of copper? (a) 3.83 x 103 (b) 1.46 x 10-2 (d) 5.85 x 10-3 (c) 1.79 x 10-2 2.

Answer 1

The ratio of the young's modulus of steel and copper is
`1.79*10^(-2)`

(c) is correct option.

Step-by-step explanation:

Given that,

Length of steel wire = 4.7 m

Cross section
`A = 3*10^(-3)\ m^2`

Length of copper wire = 3.5 m

Cross section
`A = 4*10^(-5)\ m^2`

We need to calculate the ratio of young's modulus of steel and copper

Using formula of young's modulus for steel wire

`Y=((F)/(A))/((\Delta l)/(l))`

`Y_(s)=(Fl_(s))/(A_(s)\Delta l)`....(I)

The young's modulus for copper wire

`Y_(c)=(Fl_(c))/(A_(c)\Delta l)`....(II)

From equation (I) and (II)

The ratio of the young's modulus of steel and copper

`(Y_(s))/(Y_(c))=((Fl_(s))/(A_(s)\Delta l))/((Fl_(c))/(A_(c)\Delta l))`

`(Y_(s))/(Y_(c))=(A_(c)* l_(s))/(A_(s)* l_(c))`

`(Y_(s))/(Y_(c))=(4*10^(-5)*4.7)/(3*10^(-3)*3.5)`

`(Y_(s))/(Y_(c))=1.79*10^(-2)`

Hence, The ratio of the young's modulus of steel and copper is
`1.79*10^(-2)`