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A vertical metal cylinder of radius 2 cm...

A vertical metal cylinder of radius 2 cm and length 2 m is fixed art the lower end and a load of 100 kg is put on it. find a. the stress b. the strain and c. the compression of the cylinder. Young modulus of the metl `=2xx10^11Nm^-2`

Text Solution

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The correct Answer is:
A, B, C, D
`r=2cm`
`Apir^2=4picm^2`
`=4pixx10^-4m^2`
`L=2m`
`m=100kg`
`Y=2xx10^11N/m^2`
a. `rho=stress=(mg)/A`
`=((100xx10))/((4pixx10^-4))` ltbr `=7.96xx10^5N/m^2`
b. c=strain
`=rho/Y=((97.96xx10^5))/((2xx10^11))`
`=4xx10^-6`
c. Compression `Delta L=eL`
`=4xx10^-6xx2=8x10^-6m`
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