SATHEE: Mechanical Properties of Fluids

Mechanical Properties of Fluids - Result Question 3

3. Two non-mixing liquids of densities $ρ$ and $n ρ$ $(n > 1)$ 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 $p L (p < 1)$ in the denser liquid. The density $d$ is equal to :

(a) $1 + (n + 1) p ρ$

(b) $2 + (n + 1) p ρ$

(d) $1 + (n - 1) p ρ$

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Answer:

Correct Answer: 3. (d)

Solution:

(d) As we know, Pressure $P = V d g$

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

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

$\Rightarrow V ρ g = V i n σ g$

Here, $V =$ volume of body

$ρ =$ density of body

$σ =$ density of liquid

$V_{in} =$ volume of the body immersed in liquid

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Mechanical Properties of Fluids - Result Question 3

3. Two non-mixing liquids of densities ρ and nρ (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 :

Answer:

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