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)

When a uniform wire of radius $r$ is stretched by a $2kg$ weight, the increase in its length is $2.00\, mm$. If the radius of the wire is $r/2$ and other conditions remain the same, the increase in its length is .......... $mm$

The force required to stretch a wire of crosssection $1 cm ^{2}$ to double its length will be ........ $ \times 10^{7}\,N$

(Given Yong's modulus of the wire $=2 \times 10^{11}\,N / m ^{2}$ )

The Young's modulus of a rubber string $8\, cm$ long and density $1.5\,kg/{m^3}$ is $5 \times {10^8}\,N/{m^2}$, is suspended on the ceiling in a room. The increase in length due to its own weight will be

Two steel wires of same length but radii $r$ and $2r$ are connected together end to end and tied to a wall as shown. The force stretches the combination by $10\ mm$ . How far does the midpoint $A$ move ......... $mm$

There are two wire of same material and same length while the diameter of second wire is two times the diameter of first wire, then the ratio of extension produced in the wires by applying same load will be