A rod $BC$ of negligible mass fixed at end $B$ and connected to a spring at its natural length having spring constant $K = 10^4\ N/m$ at end $C$, as shown in figure. For the rod $BC$ length $L = 4\ m$, area of cross-section $A = 4 × 10^{-4}\ m^2$, Young's modulus $Y = 10^{11} \ N/m^2$ and coefficient of linear expansion $\alpha = 2.2 × 10^{-4} K^{-1}.$ If the rod $BC$ is cooled from temperature $100^oC$ to $0^oC,$ then find the decrease in length of rod in centimeter.(closest to the integer)
Diffcult
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$Y=\frac{F L}{A(L \alpha \theta-x)} \ldots(i)$ and $F=K x \ldots .(ii)$
Solving $(i) \&(\text { ii }) x=\frac{L \alpha \theta Y A}{Y A+K L}$
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