Respuesta :
Answer:
The ratio of the young's modulus of steel and copper is [tex]1.79\times10^{-2}[/tex]
(c) is correct option.
Explanation:
Given that,
Length of steel wire = 4.7 m
Cross section[tex]A = 3\times10^{-3}\ m^2[/tex]
Length of copper wire = 3.5 m
Cross section[tex]A = 4\times10^{-5}\ m^2[/tex]
We need to calculate the ratio of young's modulus of steel and copper
Using formula of young's modulus for steel wire
[tex]Y=\dfrac{\dfrac{F}{A}}{\dfrac{\Delta l}{l}}[/tex]
[tex]Y_{s}=\dfrac{Fl_{s}}{A_{s}\Delta l}[/tex]....(I)
The young's modulus for copper wire
[tex]Y_{c}=\dfrac{Fl_{c}}{A_{c}\Delta l}[/tex]....(II)
From equation (I) and (II)
The ratio of the young's modulus of steel and copper
[tex]\dfrac{Y_{s}}{Y_{c}}=\dfrac{\dfrac{Fl_{s}}{A_{s}\Delta l}}{\dfrac{Fl_{c}}{A_{c}\Delta l}}[/tex]
[tex]\dfrac{Y_{s}}{Y_{c}}=\dfrac{A_{c}\times l_{s}}{A_{s}\times l_{c}}[/tex]
[tex]\dfrac{Y_{s}}{Y_{c}}=\dfrac{4\times10^{-5}\times4.7}{3\times10^{-3}\times3.5}[/tex]
[tex]\dfrac{Y_{s}}{Y_{c}}=1.79\times10^{-2}[/tex]
Hence, The ratio of the young's modulus of steel and copper is [tex]1.79\times10^{-2}[/tex]
