MHT CET 2017 Physics Solved Paper

(b) Let L0 be the original length of the wire, after heating temperature 'T' length becomes 'L'. α be the coefficient of thermal expansion. Increase in the length of the rod
ΔL = αL0T
L = L0[1 + αT] .......(i)
Also, Young's modulus,
Y=

FL0

AΔL

.......(ii)
Using equation (i) and substituting in equation (ii), we get
Y=

F

A

⋅

L0(1+αT)

ΔL

or, ΔL=

FL0(1+αT)

A.Y

.......(iii)
From eqs. (i) and (ii),

FL0(1+αT)

AY

=αL0T
∴ F =

YAαT

(1+αT)