Embibe Experts Solutions for Chapter: Elasticity, Exercise 1: Exercise - 1

Calculate the increase in energy of a brass bar of length $0.2 \mathrm{m}$ and cross-sectional area $1 {\mathrm{cm}}^2$ when compressed with a load of $5 \mathrm{kg}-\mathrm{weight}$ along its length.
(Young’s modulus of brass $= 1.0 \times {10}^{11} \mathrm{N} {\mathrm{m}}^{-2}$ and $g= 9.8 \mathrm{m} {\mathrm{s}}^{-2}$).

When the load on a wire increased slowly from $2 \mathrm{kg}$ weight to $4 \mathrm{kg}$ weight, the elongation increases from $0.6 \mathrm{mm}$ to $1.00 \mathrm{mm}$. How much work is done during the extension of the wire? $[g= 9.8 \mathrm{m} {\mathrm{s}}^{-2}]$

The diameter of a brass rod is $4 \mathrm{mm}$ and Young’s modulus of brass is $9\times {10}^{10} \mathrm{N} {\mathrm{m}}^{-2}$. The force required to stretch it by $0.1\%$ of its length is:

A steel wire is suspended vertically from a rigid support. When loaded with a weight in air, it expands by $L_a$ and when the weight is immersed completely in water, the extension is reduced to $L_w$. Then relative density of the material of the weight is

Two wires of equal length and cross-section area suspended as shown in the figure. Their Young's modulus are $Y_1$ and $Y_2$ respectively. The equivalent Young's modulus will be

The load versus elongation graph for four wires of the same materials is shown in the figure. The thinnest wire is represented by the line:

A given quantity of a gas is at pressure $P$ and absolute temperature $T$. The isothermal bulk modulus of the gas is

A gas undergoes a process in which its pressure $P$ and volume $V$ are related as $V{P}^n=\text{constant}$. The bulk modulus of the gas in the process is