Given σ is the compressibility of water, ρ is the density of water arid k is the bulk modulus of water. What is the energy density of water at the bottom of a lake h metre deep?

Question

Given σ is the compressibility of water, ρ is the density of water arid k is the bulk modulus of water. What is the energy density of water at the bottom of a lake h metre deep? (A)  (1/2)σ (hρ g)2  (B)  (1/2)σ (hρ g)  (C)  (1/2)(hρ g/σ )  (D)  (hρ g/σ )

Tardigrade Admin · Accepted Answer

Energy density, u=(1/2)× textstress ! !× ! ! text strain u=(1/2)× textstress text ! !× ! ! text ( textstress/ textBulk textmodulus) or u=(1/2)× textcompressibility text ! !× ! ! text text(stress) text2 ∵ textStress=h e g ∴ u=(1/2)σ (h e g)2

Q. Given $σ$ is the compressibility of water, $ρ$ is the density of water arid k is the bulk modulus of water. What is the energy density of water at the bottom of a lake $h$ metre deep?

$\frac{1}{2} σ (h ρ g)^{2}$

$\frac{1}{2} σ (h ρ g)$

$\frac{1}{2} \frac{h ρ g}{σ}$

$\frac{h ρ g}{σ}$

Energy density, $u = \frac{1}{2} \times stress \times strain$
$u = \frac{1}{2} \times stress \times \frac{stress}{Bulk modulus}$
or $u = \frac{1}{2} \times compressibility \times (stress)^{2}$
$∵$ $Stress = h e g$
$∴$ $u = \frac{1}{2} σ (h e g)^{2}$

Q. Given σ is the compressibility of water, ρ is the density of water arid k is the bulk modulus of water. What is the energy density of water at the bottom of a lake h metre deep?

21​σ(hρg)2

21​σ(hρg)

21​σhρg​

σhρg​