A steel wire of lm long and $1\,m{m^2}$ cross section area is hang from rigid end. When weight of $1\,kg$ is hung from it then change in length will be given ..... $mm$ $(Y = 2 \times {10^{11}}N/{m^2})$
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One end of a metal wire is fixed to a ceiling and a load of $2 \mathrm{~kg}$ hangs from the other end. A similar wire is attached to the bottom of the load and another load of $1 \mathrm{~kg}$ hangs from this lower wire. Then the ratio of longitudinal strain of upper wire to that of the lower wire will be____________.
[Area of cross section of wire $=0.005 \mathrm{~cm}^2$, $\mathrm{Y}=2 \times 10^{11}\ \mathrm{Nm}^{-2}$ and $\left.\mathrm{g}=10 \mathrm{~ms}^{-2}\right]$
In an experiment to determine the Young's modulus, steel wires of five different lengths $(1,2,3,4$ and $5\,m )$ but of same cross section $\left(2\,mm ^{2}\right)$ were taken and curves between extension and load were obtained. The slope (extension/load) of the curves were plotted with the wire length and the following graph is obtained. If the Young's modulus of given steel wires is $x \times 10^{11}\,Nm ^{-2}$, then the value of $x$ is
An elevator cable can have a maximum stress of $7 \times 10^7\,N/m^2$ for appropriate safety factors. Its maximum upward acceleration is $1.5\,m/s^2$ . If the cable has to support the total weight of $2000\,kg$ of a loaded elevator, the minimum area of crosssection of the cable should be ....... $cm^2$ $(g = 10\,m/s^2)$
The proportional limit of steel is $8 \times 10^8 \,N / m ^2$ and its Young's modulus is $2 \times 10^{11} \,N / m ^2$. The maximum elongation, a one metre long steel wire can be given without exceeding the elastic limit is $......mm$
A wire of length $L,$ area of cross section $A$ is hanging from a fixed support. The length of the wire changes to $L_{1}$ when mass $M$ is suspended from its free end. The expression for Young's modulus is
$Assertion :$ Hollow shaft is found to be stronger than a solid shaft made of same equal material.
$Reason :$ Torque required to produce a given twist in hollow cylinder is greater than that required to twist a solid cylinder of same length and material.