Umakant Kondapure, Collin Fernandes, Nipun Bhatia, Vikram Bathula and, Ketki Deshpande Solutions for Chapter: Elasticity, Exercise 3: Competitive Thinking

The modulus of elasticity is dimensionally equivalent to

One end of a horizontal thick copper wire of length $2\mathrm{L}$ and radius $2\mathrm{R}$ is welded to an end of another horizontal thin copper wire of length $\mathrm{L}$ and radius $\mathrm{R}$. When the arrangement is stretched by applying forces at two ends, the ratio of the elongation in the thin wire to that in the thick wire is 

A thick rope of density $\rho$ and length $L$ is hung from a rigid support. The increase in length of the rope due to its own weight is $(\mathrm{Y}$ is Young's modulus) 

A wire of length $2L$ and radius $r$ is stretched between A and B without the application of any tension. If $Y$ is Young's modulus of the wire and it is stretched like ACB, then the tension in the wire will be

(Consider $d\ll L$) 

A wire elongates by $l\mathrm{mm}$ when a load $\mathrm{W}$ is hanged from it. If the wire goes over a pulley and two weights $\mathrm{W}$, each hung at the two ends, the elongation of the wire will be (in $\mathrm{mm}$) 

A pendulum made of a uniform wire of cross-sectional area $A$ has time period $T$. When an additional mass $\mathrm{M}$ is added to its bob, the time period changes to $T_{\mathrm{M}}$. If the Young's modulus of the material of the wire is $\mathrm{Y}$ then $\frac{1}{\mathrm{Y}}$ is equal to $(\mathrm{g}=$gravitational acceleration) 

Two rods of different materials having coefficients of linear expansion ${\alpha }_1,{\alpha }_2$ and Young's modulii $Y_1$ and $Y_2$ respectively are fixed between two rigid massive walls. The rods are heated such that they undergo the same increase in temperature. There is no bending of rods. If ${\alpha }_1:{\alpha }_2=2:3,$ the thermal stress developed in the two rods are equally provided. $Y_1:Y_2$ is equal to

The stress along the length of a rod (with rectangular cross-section) is 1% of the Young's modulus of its material. What is the approximate percentage of change of its volume? (Poisson's ratio of the material of the rod is 0.3)