An object is taken $1.0\,km$ deep in sea. Density of sea $= 1.025 \times 10^3\,kg/m^3$ , Bulk modulus of object $= 1.6 \times 10^6\, KPa$ Find out percentage change in density of object $....... \%$
Medium
Download our app for free and get started
$\mathrm{B}=\frac{-\mathrm{P}}{\frac{\Delta \mathrm{V}}{\mathrm{V}}} {\rho \mathrm{V}=\mathrm{const}}$
${\frac{\Delta \rho}{\rho}=-\frac{\Delta \mathrm{V}}{\mathrm{V}}}$$\frac{\Delta \rho}{\rho}=\frac{\mathrm{P}}{\mathrm{B}}=\frac{\mathrm{dgh}}{\mathrm{B}}=\frac{1.025 \times 10^{3} \times 10 \times 10^{3}}{1.6 \times 10^{6} \times 10^{3}}=0.64 \times 10^{-2}$
$\%$ change $=\frac{\Delta \rho}{\rho} \times 100=0.64 \%$
${\frac{\Delta \rho}{\rho}=-\frac{\Delta \mathrm{V}}{\mathrm{V}}}$$\frac{\Delta \rho}{\rho}=\frac{\mathrm{P}}{\mathrm{B}}=\frac{\mathrm{dgh}}{\mathrm{B}}=\frac{1.025 \times 10^{3} \times 10 \times 10^{3}}{1.6 \times 10^{6} \times 10^{3}}=0.64 \times 10^{-2}$
$\%$ change $=\frac{\Delta \rho}{\rho} \times 100=0.64 \%$
Download our appand get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
Similar Questions
- 1A copper wire of length $4.0m$ and area of cross-section $1.2\,c{m^2}$ is stretched with a force of $4.8 \times {10^3}$ $N.$ If Young’s modulus for copper is $1.2 \times {10^{11}}\,N/{m^2},$ the increase in the length of the wire will beView Solution
- 2Four identical hollow cylindrical columns of mild steel support a big structure of mass $50 \times 10^{3} {kg}$, The inner and outer radii of each column are $50\; {cm}$ and $100 \;{cm}$ respectively. Assuming uniform local distribution, calculate the compression strain of each column. [Use $\left.{Y}=2.0 \times 10^{11} \;{Pa}, {g}=9.8\; {m} / {s}^{2}\right]$View Solution
- 3Wires $A$ and $B$ are made from the same material. $A$ has twice the diameter and three times the length of $B.$ If the elastic limits are not reached, when each is stretched by the same tension, the ratio of energy stored in $A$ to that in $B$ isView Solution
- 4View SolutionThe Poisson's ratio cannot have the value
- 5A rod of length $L$ at room temperature and uniform area of cross section $A$, is made of a metal having coefficient of linear expansion $\alpha {/^o}C$. It is observed that an external compressive force $F$, is applied on each of its ends, prevents any change in the length of the rod, when it temperature rises by $\Delta \,TK$. Young’s modulus, $Y$, for this metal isView Solution
- 6A material has Poisson's ratio $0.50.$ If a uniform rod of it suffers a longitudinal strain of $2 \times {10^{ - 3}}$, then the percentage change in volume isView Solution
- 7A thin $1 \,m$ long rod has a radius of $5\, mm$. A force of $50\,\pi kN$ is applied at one end to determine its Young's modulus. Assume that the force is exactly known. If the least count in the measurement of all lengths is $0.01\, mm$, which of the following statements is false ?View Solution
- 8An object is taken $1.0\,km$ deep in sea. Density of sea $= 1.025 \times 10^3\,kg/m^3$ , Bulk modulus of object $= 1.6 \times 10^6\, KPa$ Find out percentage change in density of object....... $\%$View Solution
- 9A copper wire and a steel wire of the same diameter and length are connected end to end and a force is applied, which stretches their combined length by $1\, cm$. The two wires will haveView Solution
- 10A rubber cord catapult has cross-sectional area $25\,m{m^2}$ and initial length of rubber cord is $10\,cm.$ It is stretched to $5\,cm.$ and then released to project a missile of mass $5gm.$ Taking ${Y_{rubber}} = 5 \times {10^8}N/{m^2}$ velocity of projected missile is ......... $ms^{-1}$View Solution