Two wires $A$ and $B$ of same length, same radius and same Young's modulus are heated to the same range of temperatures. If the coefficient of linear expansion of $A$ is $\frac{3}{2}$ times that of $B$, then the ratio of the thermal stresses produced in the two wires $A$ and $B$ is

To double the length of an iron wire having $0.5 \, cm^2$ area of cross-section,the required force will be $(Y = 10^{12} \, dyne/cm^2)$.

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 $g = 9.8 \; m/s^2$)

On applying a stress of $20 \times 10^8 \ N/m^2$,the length of a perfectly elastic wire is doubled. Its Young's modulus will be:

The length of a wire becomes $l_1$ and $l_2$ when $100\,N$ and $120\,N$ tensions are applied respectively. If $10l_2 = 11l_1$,the natural length of the wire will be $\frac{1}{x} l_1$. Here,the value of $x$ is ........

Young's moduli of two wires $A$ and $B$ are in the ratio $7 : 4$. Wire $A$ is $2\, m$ long and has radius $R$. Wire $B$ is $1.5\, m$ long and has radius $2\, mm$. If the two wires stretch by the same length for a given load,then the value of $R$ is close to ......... $mm$.