Stress required in a wire to produce $0.1\%$ strain is $4 \times10^8\, N/m^2$. Its yound modulus is $Y_1$. If stress required in other wire to produce $0.3\%$ strain is $6 \times 10^8\, N/m^2$. Its young modulus is $Y_2$. Which relation is correct
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A steel rod of length $1\,m$ and cross sectional area $10^{-4}\,m ^2$ is heated from $0^{\circ}\,C$ to $200^{\circ}\,C$ without being allowed to extend or bend. The compressive tension produced in the rod is $........\times 10^4\,N$ (Given Young's modulus of steel $=2 \times 10^{11}\,Nm ^{-2}$, coefficient of linear expansion $=10^{-5}\, K ^{-1}$.
Two exactly similar wires of steel and copper are stretched by equal forces. If the total elongation is $2 \,cm$, then how much is the elongation in steel and copper wire respectively? Given, $Y_{\text {steel }}=20 \times 10^{11} \,dyne / \ cm ^2$, $Y_{\text {copper }}=12 \times 10^{11} \,dy ne / \ cm ^2$
The elastic limit of brass is $3.5 \times 10^{10}\,N / m ^2$. Find the maximum load that can be applied to a brass wire of $0.75\,mm$ diameter without exceeding the elastic limit$.......\times 10^4\,N$
A uniform wire (Young's modulus $2 \times 10^{11}\, Nm^{-2}$ ) is subjected to longitudinal tensile stress of $5 \times 10^7\,Nm^{-2}$ . If the over all volume change in the wire is $0.02\%,$ the fractional decrease in the radius of the wire is close to
Two wires $A$ and $B$ of same length and of same material have radii $r_1$ and $r_2$ respectively. Their one end is fixed with a rigid support and at other end equal twisting couple is applied. Then ratio of the angle of twist at the end of $A$ and the angle of twist at the end of $B$ will be ..............