A rigid bar of mass $15\,kg$ is supported symmetrically by three wire each of $2 \,m$ long. These at each end are of copper and middle one is of steel. Young's modulus of elasticity for copper and steel are $110 \times 10^9 \,N / m ^2$ and $190 \times 10^9 \,N / m ^2$ respectively. If each wire is to have same tension, ratio of their diameters will be ............
$\sqrt{\frac{11}{19}}$
$\sqrt{\frac{30}{11}}$
$\sqrt{\frac{19}{11}}$
$\sqrt{\frac{11}{30}}$
If the ratio of lengths, radii and Young's moduli of steel and brass wires in the figure are $a, b$ and $c$ respectively, then the corresponding ratio of increase in their lengths is
Four identical hollow cylindrical columns of mild steel support a big structure of mass $50 \times 10^{3} {kg}$, The inner and outer radii of each column are $50\; {cm}$ and $100 \;{cm}$ respectively. Assuming uniform local distribution, calculate the compression strain of each column. [Use $\left.{Y}=2.0 \times 10^{11} \;{Pa}, {g}=9.8\; {m} / {s}^{2}\right]$
The load versus elongation graph for four wires of same length and the same material is shown in figure. The thinnest wire is represented by line
The interatomic distance for a metal is $3 \times {10^{ - 10}}\,m$. If the interatomic force constant is $3.6 \times {10^{ - 9}}\,N/{{\buildrel _{\circ} \over {\mathrm{A}}}}$, then the Young's modulus in $N/{m^2}$ will be
$A$ rod of length $1000\, mm$ and coefficient of linear expansion $a = 10^{-4}$ per degree is placed symmetrically between fixed walls separated by $1001\, mm$. The Young’s modulus of the rod is $10^{11} N/m^2$. If the temperature is increased by $20^o C$, then the stress developed in the rod is ........... $MPa$