Mechanical Properties of Fluids - Result Question 3

«««< HEAD:content/english/neet-pyq-chapterwise/physics/mechanical-properties-of-fluids/mechanical-properties-of-fluids-result-question-3.md

3. Two non-mixing liquids of densities $\rho$ and $n \rho$ $(n>1)$ are put in a container. The height of each liquid is h. A solid cylinder of length $L$ and density $d$ is put in this container. The cylinder floats with its axis vertical and length $pL(p<1)$ in the denser liquid. The density $d$ is equal to :

======= ####3. Two non-mixing liquids of densities $\rho$ and $n \rho$ $(n>1)$ are put in a container. The height of each liquid is h. A solid cylinder of length $L$ and density $d$ is put in this container. The cylinder floats with its axis vertical and length $pL(p<1)$ in the denser liquid. The density $d$ is equal to :

3e0f7ab6f6a50373c3f2dbda6ca2533482a77bed:content/english/neet-pyq-chapterwise/physics/mechanical-properties-of-fluids/mechanical-properties-of-fluids—result-question-3.md (a) ${1+(n+1) p} \rho$

(b) ${2+(n+1) p} \rho$

(c) ${2+(n-1) p} \rho$

(d) ${1+(n-1) p} \rho$

Show Answer

Answer:

Correct Answer: 3. (d)

Solution:

  1. (d) As we know, Pressure $P=Vdg$

Here, $L A d g=(p L) A(n \rho) g+(1-p) L A \rho g$ $\Rightarrow d=(1-p) \rho+pn \rho=[1+(n-1) p] \rho$

When a body of volume $V$ floats in a liquid then Weight of the body $=$ up thrust

$\Rightarrow V \rho g=Vin \sigma g$

Here, $V=$ volume of body

$\rho=$ density of body

$\sigma=$ density of liquid

$V _{\text{in }}=$ volume of the body immersed in liquid