Answer:
The length of rod is 9.04 cm
Step-by-step explanation:
We are given that an iron rod is made from 1kg of iron.
We are also given that the linear density of the rod x centimeters from that end is [tex]p(x)=\frac{1+x}{50}[/tex]
To Find length of rod
[tex]\int\limits^L_0 {e} \, dx=1[/tex]
[tex]\int\limits^L_0 {\frac{1+x}{50}} \, dx=1[/tex]
[tex]\frac{1}{50}[\frac{(1+x)^2}{50}]\Big|^L_0=1[/tex]
[tex]\frac{1}{100}[(1+L)^2-(1-0)^2]=1[/tex]
[tex](1+L)^2-1=100[/tex]
[tex](1+L)^2=101[/tex]
[tex]1+L=\sqrt{101}[/tex]
[tex]L=\sqrt{101}-1[/tex]
[tex]L=9.04[/tex]
Hence the length of rod is 9.04 cm
