A U tube contains water and methylated spirit | vedclass

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(B) As the mercury columns in the two arms of the $U$ tube are at the same level,the pressure exerted by the liquid columns above the mercury must be

Vedclass · Accepted Answer

$0.8$

Vedclass · Answer

(B) As the mercury columns in the two arms of the $U$ tube are at the same level,the pressure exerted by the liquid columns above the mercury must be equal.Let $ho_w$ be the density of water and $ho_s$ be the density of spirit.Let $h_w = 10\,cm$ be the height of the water column and $h_s = 12.5\,cm$ be the height of the spirit column.Equating the pressures at the mercury interface:$P_{	ext{water}} = P_{	ext{spirit}}$$ho_w h_w g = ho_s h_s g$Rearranging for the density of spirit:$ho_s = \frac{h_w}{h_s} ho_w$The relative density of spirit is defined as the ratio of the density of spirit to the density of water:$	ext{Relative Density} = \frac{ho_s}{ho_w} = \frac{h_w}{h_s}$Substituting the given values:$	ext{Relative Density} = \frac{10\,cm}{12.5\,cm} = \frac{100}{125} = 0.8$

$A$ $U$ tube contains water and methylated spirit separated by mercury. The mercury columns in the two arms are at the same level with $10\,cm$ of water in one arm and $12.5\,cm$ of spirit in the other,as shown in the figure. The relative density of the spirit is

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