A steel rod of length 6 mand diameter 20 mm is fixed between two rigid supports. The stress in the rod, when the temperature increases by `80^(@)C,` and the ends yield by 1 mm is
`(Y=2xx10^(6) kg cm^(-2), alpha = 12xx10^(-6)C^(-1))`

Options

A. 1580 kg `cm^(-2)`
B. 1706 kg` cm^(-2)`
C. 1648 kg `cm^(-2)`
D. 1983 kg `cm^(-2) `

Answer

A

Explanation

Increase in length due to rise in temperature is `Deltal = l alpha Delta theta`
`Delta l =(6) (12 xx 10^(-6)) (80) = 5760 xx 10^(-6) m = 5.76 ` mm
Of this 1 mm is allowed to expand . So net compression in the rod is `Delta l_("net") = 5.76 -1 = 4.76 ` mm
Compressive strain in the rod is `(Deltal_(net))/(l) = (4.76 xx 10^(-3))/(6) = 7.9 xx 10^(-4)`
Stress = Y ( strain ) = `2xx 10^(6) xx 7.9 xx 10^(-4) = 1580 kg cm^(-2)`