Two masses $m_1$ and $m_2$ are connected by a light string passing over a pulley as shown in the figure. If the cross-sectional area of the string is $S$,its length is $L$,and its Young's modulus is $Y$,what is the elongation in the string?

$A$ steel wire of length $20 \text{ cm}$ and area of cross-section $1 \text{ mm}^2$ is tied rigidly at both the ends. When the temperature of the wire is changed from $40^{\circ} \text{C}$ to $20^{\circ} \text{C}$, find the change in its tension. Given, the coefficient of linear expansion for steel is $\alpha = 1.1 \times 10^{-5} {}^{\circ} \text{C}^{-1}$ and Young's modulus of steel is $Y = 2.0 \times 10^{11} \text{ N/m}^2$. (in $\text{ N}$)

$A$ $0.1 \,kg$ mass is suspended from a wire of negligible mass. The length of the wire is $1 \,m$ and its cross-sectional area is $4.9 \times 10^{-7} \,m^2$. If the mass is pulled a little in the vertically downward direction and released, it performs simple harmonic motion of angular frequency $140 \,rad \,s^{-1}$. If the Young's modulus of the material of the wire is $n \times 10^9 \,N \,m^{-2}$, the value of $n$ is

Four identical hollow cylindrical columns of mild steel support a big structure of mass $50,000 \; kg$. The inner and outer radii of each column are $30 \; cm$ and $60 \; cm$ respectively. Assuming the load distribution to be uniform,calculate the compressional strain of each column. (Take Young's modulus of mild steel $Y = 2.0 \times 10^{11} \; Pa$ and $g = 9.8 \; m/s^2$)

Two wires of equal lengths are made of the same material. Wire $A$ has a diameter that is twice as that of wire $B$. If identical weights are suspended from the ends of these wires,the increase in length is

The ratio of diameters of two wires of the same material is $n : 1$. The length of each wire is $4 \ m$. On applying the same load,the increase in length of the thin wire will be: