A steel rod has a radius of $20\,mm$ and a length of $2.0\,m$. A force of $62.8\,kN$ stretches it along its length. Young's modulus of steel is $2.0 \times 10^{11}\,N / m ^2$. The longitudinal strain produced in the wire is $..........\times 10^{-5}$
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Two steel wires having same length are suspended from a ceiling under the same load. If the ratio of their energy stored per unit volume is $1: 4,$ the ratio of their diameters is
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
Increase in length of a wire is $1\, mm$ when suspended by a weight. If the same weight is suspended on a wire of double its length and double its radius, the increase in length will be ........ $mm$
A rod is fixed between two points at $20°C$. The coefficient of linear expansion of material of rod is $1.1 \times {10^{ - 5}}/^\circ C$ and Young's modulus is $1.2 \times {10^{11}}\,N/m$. Find the stress developed in the rod if temperature of rod becomes $10°C$
Two wires of the same material (Young's modulus $Y$ ) and same length $L$ but radii $R$ and $2R$ respectively are joined end to end and a weight $W$ is suspended from the combination as shown in the figure. The elastic potential energy in the system is
Which of the following curve represents the correctly distribution of elongation $(y)$ along heavy rod under its own weight $L \rightarrow$ length of rod, $x \rightarrow$ distance of point from lower end?
The bulk modulus of a gas is defined as $B=-V d p / d V$. For an adiabatic process the variation of $B$ is proportional to $p^n$. For an ideal gas $n$ is