G L Mittal and TARUN MITTAL Solutions for Chapter: Elasticity, Exercise 2: NUMERICALS

A body of $10 \mathrm{kg}$ tied at one end of  $0.3 \mathrm{m}$ wire is rotated in a horizontal circle. The area of cross-section of wire is ${10}^{-6} {\mathrm{m}}^2$ and the breaking stress is $4.8\times {10}^7 \mathrm{N} {\mathrm{m}}^2$. By how much maximum angular speed can the body be rotated?

A metallic wire has a radius of  $0.2 \mathrm{mm}$. How much force is required to have an increase of $0.2\%$ in its length? $\left(Y=9.0\times {10}^{10}.\right)$

If a stress of $1 \mathrm{kg} \mathrm{wt}/{\mathrm{mm}}^2$ is applied on a wire, then what will be the percentage increase in the length of the wire? $(Y=1.0\times {10}^{11} \mathrm{N} {\mathrm{m}}^{-2}$ and $1 \mathrm{kg} \mathrm{wt}=9.8 \mathrm{N})$

A brass rod of length and area of cross-section $2 {\mathrm{cm}}^2$ is compressed by a force of  $5 \mathrm{kg}-\mathrm{wt}$ along its length. Determine the increase in the length of the rod. Young's modulus of brass is $1.4\times {10}^{11} \mathrm{N} {\mathrm{m}}^{-1}$.

A fluid of volume $1.5\times {10}^{-3} {\mathrm{m}}^3$, when subjected to a pressure change of $5.0\times {10}^6 {\mathrm{Nm}}^{-2}$ has its volume reduced by $3.0\times {10}^{-7} {\mathrm{m}}^3$. Find the coefficient of bulk modulus of the fluid.

$1 {\mathrm{m}}^3$ of water is taken from the surface of a lake to a depth of $200 \mathrm{m}$ inside the lake. What will be the change in its volume if the bulk modulus of elasticity of water is $22000$ atmospheres? (Density of water $=1\times {10}^3 \mathrm{kg} {\mathrm{m}}^{-3}$, atmosphere pressure $={10}^5 \mathrm{N} {\mathrm{m}}^{-2}$ and $g=10 {\mathrm{ms}}^{-2}$.)

A wire of length $1.0 \mathrm{m}$ bas area of cross-section $0.1 {\mathrm{cm}}^2$. The Young's modulus of material of the wire is $2.5\times {10}^{11} {\mathrm{Nm}}^{-2}$ and coefficient of linear thermal expansion is $2\times {10}^{-5}° {\mathrm{C}}^{-1}$. The wire is clamped between two rigid supports and its temperatures is decreased by $10° \mathrm{C}$. Calculate the tension developed in it.

The area of cross-section of metal rod is $1 {\mathrm{cm}}^2$. It is clamped tightly at its two ends at $0°\mathrm{C}$. The rod is heated to $100°\mathrm{C}$. Calculate the tension produced at its two ends. Coefficient of linear expansion of metal is $1.2\times {10}^{-5}°{\mathrm{C}}^{-1}$ and Young's modulus is $2.0\times {10}^{11} \mathrm{N} {\mathrm{m}}^{-2}$.