A wire of cross-sectional area A at temperature T is held taut with negligible tension between two rigid supports. If the wire is cooled to a temperature (T−ΔT), what tension is developed in the wire ? The coefficient of linear expansion is α and Young's modulus of the wire is Y
see full answer
High-Paying Jobs That Even AI Can’t Replace — Through JEE/NEET
🎯 Hear from the experts why preparing for JEE/NEET today sets you up for future-proof, high-income careers tomorrow.
An Intiative by Sri Chaitanya
a
Y A α ΔT
b
Yα ΔT/A
c
A α ΔT/Y
d
YA/α ΔT
answer is A.
(Unlock A.I Detailed Solution for FREE)
Best Courses for You
JEE
NEET
Foundation JEE
Foundation NEET
CBSE
Detailed Solution
Let I be the length of the wire at temperature T. If ∆l be the contraction in length when the temperature falls by ∆T, then Δl=αlΔTStrain in wire =(Δl/l)=αΔTNow Y= stress strain =(F/A)Δl/l=FlAΔlSo, tension in the wire is given by F=Y A Δll=Y A α ΔT