Questions

# Two non-mixing liquids of densities $\rho$ and  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 $pL$ in the denser liquid. The density $d$ is equal to

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a
{2+(n-1)p}ρ
b
{1+(n-1)p}ρ
c
{1+(n+1)p}ρ
d
{2+(n+1)p}ρ

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detailed solution

Correct option is B

d=density of cylinder A=area of cross-section of cylinder using law of floatation,Using law of floatation, Weight of cylinder = Upthrust by two liquidsL×A×d×g=nρ×(pL×A)g+ρ(L-pL)Agd=npρ+ρ(1-p)=(np+1-p)ρd={1+(n-1)p}ρ

Similar Questions

Consider the following statements
(A) Specific gravity of a fluid is a dimensionless quantity.
(B) It is the ratio of density of fluid to the density of water.
Select the correct option.
(a) (A) is false but (B) is true.
(b) Both (A) and (B) are true.
(c ) (A) is true but (B) is false.
(d) Both (A) and (B) are false.

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