Consider a vessel filled with a liquid up to | vedclass

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

Question

(D) The pressure variation in a fluid with varying density is given by the hydrostatic law: $dP = -\rho(z) g dz$.Integrating from the bottom ($z=0$,$P

Vedclass · Accepted Answer

$\frac{5}{3} \rho_0 g H$

Vedclass · Answer

(D) The pressure variation in a fluid with varying density is given by the hydrostatic law: $dP = -\rho(z) g dz$.Integrating from the bottom ($z=0$,$P=P_1$) to the top ($z=H$,$P=P_2$):$\int_{P_1}^{P_2} dP = -\int_{0}^{H} \rho(z) g dz$$P_2 - P_1 = -g \int_{0}^{H} \rho_0 \left[ 2 - \left( \frac{z}{H} \right)^2 \right] dz$$P_1 - P_2 = g \rho_0 \int_{0}^{H} \left( 2 - \frac{z^2}{H^2} \right) dz$$P_1 - P_2 = g \rho_0 \left[ 2z - \frac{z^3}{3H^2} \right]_{0}^{H}$$P_1 - P_2 = g \rho_0 \left( 2H - \frac{H^3}{3H^2} \right)$$P_1 - P_2 = g \rho_0 \left( 2H - \frac{H}{3} \right)$$P_1 - P_2 = g \rho_0 \left( \frac{5H}{3} \right) = \frac{5}{3} \rho_0 g H$.

Similar Questions

Is pressure a scalar or a vector quantity? Explain.

Density of ice is $\rho$ and that of water is $\sigma$. What will be the decrease in volume when a mass $M$ of ice melts?

When two metals of equal volume are mixed,the relative density of the mixture is $4$. When equal masses of these two metals are mixed,the relative density of the mixture is $3$. What are the relative densities of the two metals?

In making an alloy,a substance of specific gravity $s_1$ and mass $m_1$ is mixed with another substance of specific gravity $s_2$ and mass $m_2$. Then,the specific gravity of the alloy is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module