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In the figure...

Question

In the figure shown, the heavy cylinder (radius R) resting on a smooth surface separates two liquids of densities $2 ρ$ and $3 ρ$ . The height 'h' for the equilibrium of cylinder must be.

3 R / 2

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R \sqrt{\frac{3}{2}}

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R \sqrt{2}

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None of these

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Solution

The correct option is B $R \sqrt{\frac{3}{2}}$
at Equilibrium, $ρ ₁ L ₁ A ₁ = ρ ₂ L ₂ A ₂$
L is the height of liquid
A is the area
$A ₁ = h \times l$
$A ₂ = R \times l$
$2 ρ \times h \times (h \times l) = 3 ρ \times R \times (R \times l)$
$2 h ² = 3 R ²$
$h$ = $R \sqrt{\frac{3}{2}}$

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In the figure shown, the heavy cylinder (radius R) resting on a smooth surface separates two liquids of densities 2ρ and 3ρ. The height 'h' for the equilibrium of cylinder must be.

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