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Question

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

A
{1+(n1)p}p
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B
{1+(n+1)p}p
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C
{2+(n+1)p}p
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D
{2(n+1)p}p
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Solution

## The correct option is A {1+(n−1)p}pd=densityofcylinderA=areaofcross−sectionalofcylinderUsinglawoffloation,weightofcylinder=upthrustbytwoliquidsL×A×d×g=nρ×(pL×A)g+ρ(L−pL)Agd=npρ+ρ(1−p)=(np+1−p)ρd={1+(n−1)p}ρHence,option (A) is correct answer.

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