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

If the pressure on a body is increased from $200 \text{ kPa}$ to $250 \text{ kPa}$,the volume of the body decreases by $0.25 \%$. The compressibility of the material of the body is (in $m^2 \text{ N}^{-1}$)

Bulk modulus was first defined by

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

$A$ uniform cube is subjected to volume compression. If each side is decreased by $1\%$,then the bulk strain is

When a pressure of $100 \, atm$ is applied to a rubber ball,its volume decreases by $0.01 \%$. What is the bulk modulus of the rubber?

Vedclass Test Series

Exam Paper Generator

Online Exam Module