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A metal rod of Young's modulus 2 xx 10 ^...

A metal rod of Young's modulus `2 xx 10 ^(10) Nm ^(-2),` undergoes longitudinal strain of 1%, the potential energy per unit volume stored in rod is ....... `Jm^(-3).`

A

`10 ^(6)`

B

`10^(8)`

C

`2xx10 ^(6)`

D

`2xx10^(8)`

Text Solution

Verified by Experts

The correct Answer is:
A
The potnetial energy per unit volume
`u = 1/2 xx` stress `xx` strain
`=1/2 xx` Young modulus `xx("strain")^(2)`
`(because` stress `= Y xx` strain)
`=1/2 xx Y ((Delta l )/(l )) ^(2) `
` therefore u = 1/2 xx 2 xx 10 ^(10) xx (0.01) ^(2)`
`therefore u = 1 xx 10 ^(6)`
`=10^(6) Jm^(-3)`
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