A sphere contracts in volume by $0.01 \%$ when taken to the bottom of sea $1 \,km$ deep. Find Bulk modulus of the material of sphere ........... $N / m ^2$
Easy
Download our app for free and get started
(c)
Pressure at bottom of sea $=\rho_w g h$
$\rho_w=1000 \,kg / m ^3=1 \,g / cc , \quad g=9.8 \,m / s ^2, h=1000 \,m$
$P=10^3 \times 9.8 \times 1000 \,N / m ^2$
$\text { Now } \frac{-\Delta V}{V}=\frac{P}{B} \quad\left\{\frac{-\Delta V}{V}=\frac{0.01}{100}\right. \text { (given) }$
$\frac{0.01}{100}=\frac{10^3 \times 9.8 \times 1000}{B}$
$B=9.8 \times 10^{10} \,N / m ^2$
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
- 1Young's moduli of the material of wires $A$ and $B$ are in the ratio of $1: 4$, while its area of cross sections are in the ratio of $1: 3$. If the same amount of load is applied to both the wires, the amount of elongation produced in the wires $A$ and $B$ will be in the ratio ofView Solution
[Assume length of wires $A$ and $B$ are same]
- 2A rigid bar of mass $15\,kg$ is supported symmetrically by three wire each of $2 \,m$ long. These at each end are of copper and middle one is of steel. Young's modulus of elasticity for copper and steel are $110 \times 10^9 \,N / m ^2$ and $190 \times 10^9 \,N / m ^2$ respectively. If each wire is to have same tension, ratio of their diameters will be $ ............$View Solution
- 3A suspended long metal wire is stretched a small distance $x$ by a load $W$ in newton suspended at the other end. Select the best answer out of the followingView Solution
- 4A glass slab is subjected to a pressure of $10\, atm$. The fractional change in its volume is (Bulk modulus of glass $= 37 \times 10^9\, N\, m^{-2}$, $1\, atm = 1 \times 10^5\, N\, m^{-2}$)View Solution
- 5A wire can be broken by applying a load of $200\, N$. The force required to break another wire of the same length and same material, but double in diameter, is .......... $N$View Solution
- 6If the Bulk modulus of lead is $8.0 \times 10^9 \,N / m ^2$ and the initial density of the lead is $11.4 \,g / cc$, then under the pressure of $2.0 \times 10^8 \,N / m ^2$, the density of the lead is $............. g / cc$View Solution
- 7Join the relation of physical quantities in Column$-I$ to the details given in Column$-II$ appropriately :View Solution
Column $-I$ Column $-II$ $(a)$ Stress $\propto $ Strain $(i)$ $M^1\,L^{-1}\,T^{-2}$ $(b)$ Dimensional formula for compressibility $(ii)$ $M^{-1}\,L^{1}\,T^{-2}$ $(iii)$ Poisson’s ratio $(iv)$ Hooke’s law - 8Match List-$I$ with List-$II$ :View Solution
List-$I$ List-$II$ $(A)$ A force thatrestores anelastic body of unit area to its original state $(I)$ Bulkmodulus $(B)$ Two equal andopposite forcesparallel toopposite faces $(II)$Young'smodulus $(C)$Forcesperpendiculareverywhere tothe surface perunit areasameeverywhere $(III)$ Stress $(D)$Two equal andopposite forceperpendicular toopposite faces $(IV)$ Shearmodulus Choose the correct answer from the options given below:
- 9A wire extends by $1 mm$ when a force is applied. Double the force is applied to another wire of same material and length but half the radius of cross-section. The elongation of the wire in mm will be ........View Solution
- 10Steel and copper wires of same length are stretched by the same weight one after the other. Young's modulus of steel and copper are $2 \times {10^{11}}\,N/{m^2}$ and $1.2 \times {10^{11}}\,N/{m^2}$. The ratio of increase in lengthView Solution