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The adjacent graph shows the extension $(\Delta l)$ of a wire of length $1\, m$ suspended from the top of a roof at one end and with a load $W$ connected to the other end. If the cross-sectional area of the wire is $10^{-6}\, m^2$, calculate the Young’s modulus of the material of the wire.
An aluminum rod (Young's modulus $ = 7 \times {10^9}\,N/{m^2})$ has a breaking strain of $0.2\%$. The minimum cross-sectional area of the rod in order to support a load of ${10^4}$Newton's is
The work done in increasing the length of a $1$ $metre$ long wire of cross-section area $1\, mm^2$ through $1\, mm$ will be ....... $J$ $(Y = 2\times10^{11}\, Nm^{-2})$
The bulk moduli of ethanol, mercury and water are given as $0.9, 25$ and $2 .2$ respectively in units of $10^9\, Nm^{-2}$ . For a given value of pressure, the fractional compression in volume is $\frac{{\Delta V}}{V}$. Which of the following statements about $\frac{{\Delta V}}{V}$ for these three liquids is correct ?
Given : $\sigma$ is the compressibility of water, $\rho$ is the density of water and $K$ is the bulk modulus of water. What is the energy density of water at the bottom of a lake $‘h’$ metre deep ?
Two wires of same length and radius are joined end to end and loaded. The Young's modulii of the materials of the two wires are $Y_{1}$ and $Y_{2}$. The combination behaves as a single wire then its Young's modulus is:
Two similar wires under the same load yield elongation of $0.1$ $mm$ and $0.05$ $mm$ respectively. If the area of cross- section of the first wire is $4m{m^2},$ then the area of cross section of the second wire is..... $mm^2$