A substance breaks down by a stress of $10^6 N/m^2$. If the density of the material of the wire is $3×10^3 kg/m^3$, then the length of the wire of the substance which will break under its own weight when suspended vertically, is ......... $m$
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A square aluminium (shear modulus is $25 \times 10^{9}\,Nm ^{-2}$ ) slab of side $60\,cm$ and thickness $15\,cm$ is subjected to a shearing force (on its narrow face) of $18.0 \times 10^{4}\,N$. The lower edge is riveted to the floor. The displacement of the upper edge is $.......\mu\,m$.
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
Each of three blocks $P$, $Q$ and $R$ shown in figure has a mass of $3 \mathrm{~kg}$. Each of the wire $A$ and $B$ has cross-sectional area $0.005 \mathrm{~cm}^2$ and Young's modulus $2 \times 10^{11} \mathrm{~N} \mathrm{~m}^{-2}$. Neglecting friction, the longitudinal strain on wire $B$ is____________ $\times 10^{-4}$. $\left(\right.$ Take $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2$ )
A cubical solid aluminium (bulk modulus $=-V \frac{ dP }{ dV }=70 GPa$ ) block has an edge length of $1 m$ on the surface of the earth. It is kept on the floor of a $5 km$ deep ocean. Taking the average density of water and the acceleration due to gravity to be $10^3 kg m ^{-3}$ and $10 ms ^{-2}$, respectively, the change in the edge length of the block in $mm$ is . . . . .