Mechanical Properties of Fluids - Result Question 3
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 :
(a) ${1+(n+1) p} \rho$
(b) ${2+(n+1) p} \rho$
(c) ${2+(n-1) p} \rho$
(d) ${1+(n-1) p} \rho$
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Answer:
Correct Answer: 3. (d)
Solution:
- (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
