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The area of a cross-section of steel wire is $0.1\,\,cm^2$ and Young's modulus of steel is $2\,\times \,10^{11}\,\,N\,\,m^{-2}.$ The force required to stretch by $0.1\%$ of its length is ......... $N$.
If $\rho $ is the density of the material of a wire and $\sigma $ is breaking stress, the greatest length of the wire that can hang freely without breaking is
Two separate wires $A$ and $B$ are stretched by $2 \,mm$ and $4\, mm$ respectively, when they are subjected to a force of $2\, N$. Assume that both the wires are made up of same material and the radius of wire $B$ is 4 times that of the radius of wire $A$. The length of the wires $A$ and $B$ are in the ratio of $a : b$. Then $a / b$ can be expressed as $1 / x$ where $x$ is
The elastic behaviour of material for linear streass and linear strain, is shown in the figure. The energy density for a linear strain of $5 \times 10^{-4}$ is $\dots \; kJ / m ^{3}$. Assume that material is elastic upto the linear strain of $5 \times 10^{-4}$.
A metal rod of cross-sectional area $10^{-4} \,m ^{2}$ is hanging in a chamber kept at $20^{\circ} C$ with a weight attached to its free end. The coefficient of thermal expansion of the rod is $2.5 \times 10^{-6} \,K ^{-1}$ and its Young's modulus is $4 \times 10^{12} \,N / m ^{2}$. When the temperature of the chamber is lowered to $T$, then a weight of $5000 \,N$ needs to be attached to the rod, so that its length is unchanged. Then, $T$ is ............ $^{\circ} C$
Copper of fixed volume $V$ is drawn into wire of length $l$. When this wire is subjected to a constant force $F$, the extension produced in the wire is $\Delta l$. Which of the following graphs is a straight line?
If the temperature of a wire of length $2 \,m$ and area of cross-section $1 \,cm ^2$ is increased from $0^{\circ} C$ to $80^{\circ} C$ and is not allowed to increase in length, then force required for it is ............$N$ $\left\{Y=10^{10} \,N / m ^2, \alpha=10^{\left.-6 /{ }^{\circ} C \right\}}\right.$