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A metal rod of cross-sectional area $10^{-4} \,m ^{2}$ is hanging in a chamber kept at $20^{\circ} C$ with a weight attached to its free end. The coefficient of thermal expansion of the rod is $2.5 \times 10^{-6} \,K ^{-1}$ and its Young's modulus is $4 \times 10^{12} \,N / m ^{2}$. When the temperature of the chamber is lowered to $T$, then a weight of $5000 \,N$ needs to be attached to the rod, so that its length is unchanged. Then, $T$ is ............ $^{\circ} C$
A steel wire of diameter $2 \,mm$ has a breaking strength of $4 \times 10^5 \,N.$ the breaking force $......... \times 10^5 \,N$ of similar steel wire of diameter $1.5 \,mm$ ?
A uniformly tapering conical wire is made from a material of Young's modulus $Y$ and has a normal, unextended length $L.$ The radii, at the upper and lower ends of this conical wire, have values $R$ and $3R,$ respectively. The upper end of the wire is fixed to a rigid support and a mass $M$ is suspended from its lower end. The equilibrium extended length, of this wire, would equal
A steel rod of length $1\,m$ and cross sectional area $10^{-4}\,m ^2$ is heated from $0^{\circ}\,C$ to $200^{\circ}\,C$ without being allowed to extend or bend. The compressive tension produced in the rod is $........\times 10^4\,N$ (Given Young's modulus of steel $=2 \times 10^{11}\,Nm ^{-2}$, coefficient of linear expansion $=10^{-5}\, K ^{-1}$.
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 $.......\mu\,m$.