A hollow sphere of radius R is filled complet | vedclass

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

Question

(C) In the frame of the sphere,the liquid experiences a pseudo-force in the backward direction with an acceleration $a = 2g$. The effective accelerati

Vedclass · Accepted Answer

$P_0 + \rho gR\sqrt{5}$

Vedclass · Answer

(C) In the frame of the sphere,the liquid experiences a pseudo-force in the backward direction with an acceleration $a = 2g$. The effective acceleration vector $\vec{g}_{eff}$ is the vector sum of the acceleration due to gravity $\vec{g}$ (acting downwards) and the pseudo-acceleration $\vec{a}_{pseudo} = -2g\hat{i}$ (acting backwards).Thus,$\vec{g}_{eff} = -2g\hat{i} - g\hat{j}$.The magnitude of the effective acceleration is $g_{eff} = \sqrt{(2g)^2 + g^2} = \sqrt{5g^2} = g\sqrt{5}$.The pressure in the liquid varies as $P = P_{min} + ho \vec{g}_{eff} \cdot \vec{r}$,where $\vec{r}$ is the displacement vector from the point of minimum pressure to the point of interest.The minimum pressure occurs at the point furthest in the direction of $\vec{g}_{eff}$. The distance from the centre to this point is $R$.The pressure at the centre is $P_c = P_{min} + ho g_{eff} 	imes R$.Substituting the values,$P_c = P_0 + ho (g\sqrt{5}) R = P_0 + ho gR\sqrt{5}$.

Similar Questions

Three identical vessels are filled up to the same height with three different liquids $A, B$ and $C$ of densities $\rho_A, \rho_B$ and $\rho_C$ (where $\rho_A > \rho_B > \rho_C$). The pressure at the bottom of the vessels is:

Two liquids of densities $\rho_1 = 1$ and $\rho_2 = 2$ are mixed in equal masses. What is the density of the resulting mixture?

An open $U$-tube contains mercury. When $13.6 \,cm$ of water is poured into one of the arms of the tube,then the mercury rise in the other arm from its initial level is ....... $cm$

What is thrust?

$A$ force of $F = 10 \ N$ is exerted on a surface of area $A = 0.1 \ m^{2}$ at an angle of $60^{\circ}$ with the surface. Find the pressure produced on this surface.

Vedclass Test Series

Exam Paper Generator

Online Exam Module