Respuesta :
Answer:
The difference in the length of the two rods when compressed is [tex]5.4\times10^{-5}\ m[/tex].
Explanation:
Given that,
Length = 0.780 m
Diameter = 1.50 cm
Force = 4350 N
(a). For steel rod
We know ,
The young modulus for steel rod
[tex]Y=2\times10^{11}[/tex]
Using formula of young modulus
[tex]e_{s}=\dfrac{Fl}{AY}[/tex]
[tex]e_{s}=\dfrac{4350\times0.780}{3.14\times(0.75\times10^{-2})^2\times2\times10^{11}}[/tex]
[tex]e_{s}=9.6\times10^{-5}\ m[/tex]
(b). For copper rod
We know ,
The young modulus for steel rod
[tex]Y=1.1\times10^{11}[/tex]
Using formula of young modulus
[tex]e_{c}=\dfrac{Fl}{AY}[/tex]
[tex]e_{c}=\dfrac{4350\times0.780}{3.14\times(0.75\times10^{-2})^2\times1.1\times10^{11}}[/tex]
[tex]e_{c}=1.5\times10^{-4}\ m[/tex]
The difference in the length of the two rods when compressed is
[tex]difference\ in\ length=e_{c}-e_{s}[/tex]
[tex]difference\ in\ length=1.5\times10^{-4}-9.6\times10^{-5}[/tex]
[tex]difference\ in\ length =5.4\times10^{-5}\ m[/tex]
Hence, The difference in the length of the two rods when compressed is [tex]5.4\times10^{-5}\ m[/tex].
