A U-tube contains water and methylated spirit separated by mercur… - Vidyadip

MCQ

A $U-$tube contains water and methylated spirit separated by mercury. The mercury columns in the two arms are in level with $10.0\; cm$ of water in one arm and $12.5\; cm $ of spirit in the other. if $15.0\; cm$ of water and spirit each are further poured into the respective arms of the tube, what is the difference in the levels (in $cm$) of mercury in the two arms?

(the specific gravity of spirit is $0.8.)$

✓
$0.22$
B
$0.86$
C
$1.22$
D
$2.12$

✓

Answer

Correct option: A.

$0.22$

a
Height of the water column, $h_{1}=10+15=25 cm$

Height of the spirit column, $h_{2}=12.5+15=27.5 cm$

Density of water, $\rho_{1}=1 g cm ^{-3}$

Density of spirit, $\rho_{2}=0.8 g cm ^{-3}$

Density of mercury $=13.6 g cm ^{-3}$

Let $h$ be the difference between the levels of mercury in the two arms.

Pressure exerted by height $h,$ of the mercury column:

$=h \rho g =h \times 13.6 g \ldots(i)$

Difference between the pressures exerted by water and spirit:

$=h_{1} \rho_{1} g -h_{1} \rho_{1} g$

$=g(25 \times 1-27.5 \times 0.8)=3 g \ldots (i i)$

Equating equations ( $i$ ) and (ii), we get:

$13.6 hg =3 g h$

$=0.220588 \approx 0.221 cm$

Hence, the difference between the levels of mercury in the two arms is $0.221 \,cm .$

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