A uniform solid cylinder of density 0.8 g/cm^3 floats in equilibrium in a combination of two non-mix

English

Gujarati

Hindi

9-1.Fluid Mechanics

hard

A uniform solid cylinder of density $0.8$ $g/cm^3$ floats in equilibrium in a combination of two non-mixing liquid $A$ and $B$ with its axis vertical. The densities of liquid $A$ and $B$ are $0.7$ $g/cm^3$ and $1.2$ $gm/cm^3$. The height of liquid $A$ is $h_A = 1.2$ $cm$ and the length of the part of cylinder immersed in liquid $B$ is $h_B = 0.8$ $cm$. Then the length part of the cylinder in air is ....... $cm$

A

$0.21$

B

$0.25$

C

$0.35$

D

$0.4$

Solution

For equilibrium, Buoyant force $=$ weight of the body

$\Rightarrow h_{A} \rho_{A} A g+h_{B} \rho_{B} A g=\left(h_{A}+h+h_{B}\right) A \rho_{C} g$

(where $\rho_{C}=$ density of cylinder)

$h=\left(\frac{h_{A} \rho_{A}+h_{B} \rho_{B}}{\rho_{C}}\right)-\left(h_{A}+h_{B}\right)=0.25 \mathrm{cm}$

Standard 11

Physics

Share

Similar Questions

A ball of relative density $0.8$ falls into water from a height of $2$ $m$. The depth to which the ball will sink is …….. $ m$ (neglect viscous forces) :

medium

A vertical triangular plate $ABC$ is placed inside water with side $BC$ parallel to water surface as shown. The force on one surface of plate by water is (density of water is $\rho $ and atmospheric pressure $P_0$ )

hard

A fluid container is containing a liquid of density $\rho $ is accelerating upward with acceleration a along the inclined place of inclination $\alpha$ as shown. Then the angle of inclination $ \theta $ of free surface is :

normal

A metal ball of density $7800\ kg/m^3$ is suspected to have a large number of cavities . It weighs $9.8$ $kg$ when weighed directly on a balance and $1.5$ $kg$ less when immersed in water . The fraction by volume of the cavities in the metal ball is approximately ……. $\%$

hard

A uniform cylinder of length $L$ and mass $M$ having crosssectional area $A$ is suspended, with its length vertical, from a fixed point by a massless spring such that it is half submerged in a liquid of density $\sigma$ at equilibrium position. The extension $x_0$ of the spring when it is in equilibrium is

hard

(JEE MAIN-2013)