The interatomic distance for a metal is $3 \times {10^{ - 10}}\,m$. If the interatomic force constant is $3.6 \times {10^{ - 9}}\,N/{{\buildrel _{\circ} \over {\mathrm{A}}}}$, then the Young's modulus in $N/{m^2}$ will be
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A wire of length $5 \,m$ is twisted through $30^{\circ}$ at free end. If the radius of wire is $1 \,mm$, the shearing strain in the wire is ..........,.
A brass rod of length $2\,m$ and cross-sectional area $2.0\,cm^2$ is attached end to end to a steel rod of length $L$ and cross-sectional area $1.0\,cm^2$ . The compound rod is subjected to equal and opposite pulls of magnitude $5 \times 10^4\,N$ at its ends. If the elongations of the two rods are equal, then length of the steel rod $(L)$ is ........... $m$ $(Y_{Brass}=1.0\times 10^{11}\,N/m^2$ and $Y_{Steel} = 2.0 \times 10^{11}\,N/m^2)$
The pressure applied from all directions on a cube is $P$. How much its temperature should be raised to maintain the original volume $?$ The volume elasticity of the cube is $\beta $ and the coefficient of volume expansion is $\alpha $
Two wires of the same material have lengths in the ratio 1 : 2 and their radii are in the ratio $1:\sqrt 2 $. If they are stretched by applying equal forces, the increase in their lengths will be in the ratio
A material has Poisson's ratio $0.5$. If a uniform rod of it suffers a longitudinal strain of $3 \times 10^{-3}$, what will be percentage increase in volume is .......... $\%$
A wire of length $50\, cm$ and cross sectional area of $1$ sq. mm is extended by $1\, mm.$ The required work will be $(Y = 2 \times {10^{10}}\,N{m^{ - 2}})$
The work per unit volume to stretch the length by $1\%$ of a wire with cross sectional area of $1\,m{m^2}$ will be. $[Y = 9 \times {10^{11}}\,N/{m^2}]$
A steel ring of radius $r$ and cross-section area $‘A’$ is fitted on to a wooden disc of radius $R(R > r)$. If Young's modulus be $E,$ then the force with which the steel ring is expanded is