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 $1.5 \,mm$ ?
$2.3$
$2.6$
$3$
$1.5$
A compressive force, $F$ is applied at the two ends of a long thin steel rod. It is heated, simultaneously, such that its temperature increases by $\Delta T$. The net change in its length is zero. Let $l$ be the length of the rod, $A$ its area of cross- section, $Y$ its Young's modulus, and $\alpha $ its coefficient of linear expansion. Then, $F$ is equal to
Young's modulus depends upon
An equilateral triangle $ABC$ is formed by two copper rods $AB$ and $BC$ and one is aluminium rod which heated in such a way that temperature of each rod increases by $\Delta T$. Find change in the angle $\angle {ABC}$. (Coefficient of linear expansion for copper is $\alpha _1$ and for aluminium is $\alpha _2$).
A thick rope of density $\rho$ and length $L$ is hung from a rigid support. The Young's modulus of the material of rope is $Y$. The increase in length of the rope due to its own weight is
The maximum elongation of a steel wire of $1 \mathrm{~m}$ length if the elastic limit of steel and its Young's modulus, respectively, are $8 \times 10^8 \mathrm{~N} \mathrm{~m}^{-2}$ and $2 \times 10^{11} \mathrm{~N} \mathrm{~m}^{-2}$, is: