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)`)

Options

A. `10`
B. `10^(8)`
C. `2 xx 10^(8)`
D. cannot be calculated

Answer

B

Explanation

The change in length of rod due to increase in temperature in absense of walls is
`Delta l = l alpha Delta T = 1000xx10^(-4) xx 20 mm`
`=2mm`
But the rod can expand upto `1001mm` only.
As that temperature its natural length is =`1002mm`.
`:.` Compression = `1mm`.
`:.` mechanical stress
`=Y = (Delta l)/(l) = 10^(11) xx 1/1000 = 10^(8)N//m^(2)`.