A cubical solid aluminium (bulk modulus B = - | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) The pressure at depth $h$ is given by $P = ho g h$.Given $h = 5 	ext{ km} = 5000 	ext{ m}$,$ho = 10^3 	ext{ kg m}^{-3}$,and $g = 10 	ext{

Vedclass · Accepted Answer

$2.38$

Vedclass · Answer

(B) The pressure at depth $h$ is given by $P = ho g h$.Given $h = 5 	ext{ km} = 5000 	ext{ m}$,$ho = 10^3 	ext{ kg m}^{-3}$,and $g = 10 	ext{ m s}^{-2}$,the pressure is $P = 10^3 	imes 10 	imes 5000 = 5 	imes 10^7 	ext{ Pa}$.The bulk modulus $B$ is defined as $B = -V \frac{dP}{dV}$. For a cube of side $a$,$V = a^3$,so $dV = 3a^2 da$.Thus,$\frac{dV}{V} = \frac{3a^2 da}{a^3} = 3 \frac{da}{a}$.Substituting this into the bulk modulus formula: $B = -\frac{P}{3 \frac{da}{a}} \implies \frac{da}{a} = \frac{P}{3B}$.Here,$a = 1 	ext{ m}$,$P = 5 	imes 10^7 	ext{ Pa}$,and $B = 70 	imes 10^9 	ext{ Pa}$.$da = \frac{a 	imes P}{3B} = \frac{1 	imes 5 	imes 10^7}{3 	imes 70 	imes 10^9} = \frac{5}{210} 	imes 10^{-2} 	ext{ m} = \frac{1}{42} 	imes 10^{-2} 	ext{ m} \approx 0.0238 	imes 10^{-1} 	ext{ m} = 2.38 	imes 10^{-3} 	ext{ m} = 2.38 	ext{ mm}$.

Similar Questions

The only elastic modulus that applies to fluids is

$A$ sample of a liquid is kept at $1 \ atm$. It is compressed to $5 \ atm$,which leads to a change of volume of $0.8 \ cm^3$. If the bulk modulus of the liquid is $2 \ GPa$,the initial volume of the liquid was . . . . . . litre. (Take $1 \ atm = 10^5 \ Pa$)

Which of the following moduli of elasticity is possible in solids,liquids,and gases?

The average depth of the Indian Ocean is about $3000\; m$. Calculate the fractional compression,$\Delta V / V,$ of water at the bottom of the ocean,given that the bulk modulus of water is $2.2 \times 10^{9}\; N m^{-2}$. (Take $g = 10\; m s^{-2}$)

The compressibility of water is $4 \times 10^{-5}$ per unit atmospheric pressure. The decrease in volume of $100 \ cm^3$ of water under a pressure of $100 \ atm$ will be ......... $cm^3$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module