A solid spherical ball of volume -V- and density - floats on the interface of two immiscible liquids- The densities of upper and lower liquids are -1 and -2 respectively- The density of the ball if the ball floats with exactly half it volume in two liquids is-

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Standard XII

Physics

Floating

A solid spher...

Question

A solid spherical ball of volume $^{'} V^{'}$ and density $^{'} ρ^{'}$ floats on the interface of two immiscible liquids. The densities of upper and lower liquids are $ρ_{1}$ and $ρ_{2}$ respectively. The density of the ball if the ball floats with exactly half it volume in two liquids is:-

\sqrt{ρ_{1} ρ_{2}}

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\frac{ρ_{1} + ρ_{2}}{2}

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\frac{ρ_{1} (ρ_{1} + ρ_{2})}{ρ_{2}}

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\frac{(P - P_{2})}{(P_{1} - P)}

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Solution

The correct option is B $\frac{ρ_{1} + ρ_{2}}{2}$
$Acc. to given condition$
$mass of ball = mass (liq \cdot 1 + liq \cdot 2)$
$ρ v = ρ_{1} \frac{v}{2} + \frac{ρ_{2} v}{2}$
$ρ = \frac{ρ_{1} + ρ_{2}}{2}$

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A solid spherical ball of volume ′V′ and density ′ρ′ floats on the interface of two immiscible liquids. The densities of upper and lower liquids are ρ1 and ρ2 respectively. The density of the ball if the ball floats with exactly half it volume in two liquids is:-

The correct option is B ρ1+ρ22 Acc. to given condition mass of ball =mass(liq⋅1+liq⋅2)ρv=ρ1v2+ρ2v2ρ=ρ1+ρ22

A solid spherical ball of volume $^{'} V^{'}$ and density $^{'} ρ^{'}$ floats on the interface of two immiscible liquids. The densities of upper and lower liquids are $ρ_{1}$ and $ρ_{2}$ respectively. The density of the ball if the ball floats with exactly half it volume in two liquids is:-

The correct option is B $\frac{ρ_{1} + ρ_{2}}{2}$
$Acc. to given condition$
$mass of ball = mass (liq \cdot 1 + liq \cdot 2)$
$ρ v = ρ_{1} \frac{v}{2} + \frac{ρ_{2} v}{2}$
$ρ = \frac{ρ_{1} + ρ_{2}}{2}$