Question

calculate the diameter of a silver wire of length 75cm , which is extended by 1.85mm when a 10kg mass is suspended from it's end. Young modulus for silver is 7.9×10^10N/m²​

Answer 1

Answer:
`0.8\ mm`

Step-by-step explanation:

Given

length of wire
`l=75\ cm`

change in length
`\Delta l=1.85\ mm`

mass of wire
`m=10\ kg`

Young's modulus for silver
`E=7.9* 10^(10)\ N/m^2`

load on wire
`F=mg`

`F=10* 9.8=98\ kg`

change in length is given by

`\Delta l=(Pl)/(AE)`

Where A=area of cross-section

`A=(Pl)/(\Delta lE)`

`A=(98* 0.75)/(1.85* 10^(-3)* 7.9* 10^(10))`

`A=(73.5)/(14.615* 10^(7))`

`A=5.029* 10^(-7)\ m^2`

also wire is the shape of cylinder so cross-section is given by

`A=(\pi d^2)/(4)=5.029* 10^(-7)\ m^2`

`\Rightarrow d^2=(5.029* 10^(-7)* 4)/(\pi )`

`\Rightarrow d^2=64.02* 10^(-8)`

`\Rightarrow d=8* 10^(-4)\ m`

`\Rightarrow d=0.8\ mm`