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A rod of length 1000 mm and co-efficient...

A rod of length `1000 mm` and co-efficient of linear expansion `alpha = 10^(-4)` per degree celsius is placed in horizontal smooth surface symmetrically between fixed walls separated by `1001 mm `. The young's modulus of rod is `10^(11)N//m^(2)`. If the temperature is increased by `20^@C`, then the stress developed in the rod is (in ` N//m^(2)`)

A

`10^(5)`

B

`10^(8)`

C

`10^(7)`

D

`10^(6)`

Text Solution

Verified by Experts

The correct Answer is:
B
`Deltal` due to temperature rise ltbr. `= l alpha Delta theta`
`= (1000) (10^(-4))xx(20)` ltbr. `2 mm `
But `1 mm` is allowed (`1000 mm to 1001 mm `)
`:. Deltal_(epsilon) = 1 mm`
`"Stress" = Y xx "Strain"`
` (10^(11))((1 mm)/(1000 mm))`
`10^(8) N//m^(2)`
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