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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 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 $=10^{-5}\, K ^{-1}$.
$Assertion :$ 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.
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 diagram shows the change $x$ in the length of a thin uniform wire caused by the application of stress $F$ at two different temperatures $T_1$ and $T_2$. The variations shown suggest that
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 solid cube of copper of edge $10 \,cm$ subjected to a hydraulic pressure of $7 \times 10^6\, pascal$. If Bulk modulus of copper is $140 \,GPa$, then contraction in its volume will be ................ $m ^3$