In the figure shown, the heavy cylinder (radius $R$) resting on a smooth surface separates two liquids of densities $2\ \rho$ and $3\ \rho$ . The height $‘h’$ for the equilibrium of cylinder must be
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Balancing force on both sides Horizontal force acting on the cylinder can be assumed to be acting on the cross$-$sectional area in the vertical direction
$2 \mathrm{ogh} . \frac{\mathrm{h}}{2}=\frac{3 \rho \mathrm{gR.} \mathrm{R}}{2}$
$h^{2}=\frac{3}{2} R^{2}$
$\mathrm{h}=\sqrt{\frac{3}{2}} \mathrm{R}$
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