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

Answer:

The ratio of the young's modulus of steel and copper is $1.79\times10^{-2}$

(c) is correct option.

Explanation:

Given that,

Length of steel wire = 4.7 m

Cross section$A = 3\times10^{-3}\ m^2$

Length of copper wire = 3.5 m

Cross section$A = 4\times10^{-5}\ m^2$

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

Using formula of young's modulus for steel wire

$Y=\dfrac{\dfrac{F}{A}}{\dfrac{\Delta l}{l}}$

$Y_{s}=\dfrac{Fl_{s}}{A_{s}\Delta l}$....(I)

The young's modulus for copper wire

$Y_{c}=\dfrac{Fl_{c}}{A_{c}\Delta l}$....(II)

From equation (I) and (II)

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

$\dfrac{Y_{s}}{Y_{c}}=\dfrac{\dfrac{Fl_{s}}{A_{s}\Delta l}}{\dfrac{Fl_{c}}{A_{c}\Delta l}}$

$\dfrac{Y_{s}}{Y_{c}}=\dfrac{A_{c}\times l_{s}}{A_{s}\times l_{c}}$

$\dfrac{Y_{s}}{Y_{c}}=\dfrac{4\times10^{-5}\times4.7}{3\times10^{-3}\times3.5}$

$\dfrac{Y_{s}}{Y_{c}}=1.79\times10^{-2}$

Hence, The ratio of the young's modulus of steel and copper is $1.79\times10^{-2}$