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 $0.8.)$
Medium
Download our app for free and get started
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 $0.221 \,cm .$
Download our appand get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
Similar Questions
- 1In the figure shown, a liquid is flowing through a tube at the rate of $0.1\, m^3/sec$. The tube is branched into two semicircular tubes of cross-sectional area $A/3$ and $2A/3$. The velocity of liquid at $Q$ is ......... $ m/sec$ (The cross-section of the main tube $= A =10^{-2}\, m^2$ and $v_p = 20\, m/sec$)View Solution
- 2A spring balance reads $200 \,gF$ when carrying a lump of lead in air. If the lead is now immersed with half of its volume in brine solution, what will be the new reading of the spring balance? specific gravity of lead and brine are $11.4$ and $1.1$ respectively ........... $gF$View Solution
- 3The cross sectional area of a horizontal tube increases along its length linearly, as we move in the direction of flow. The variation of pressure, as we move along its length in the direction of flow ($x-$ direction), is best depicted by which of the following graphsView Solution
- 4A uniform solid cylinder of density $0.8$ $g/cm^3$ floats in equilibrium in a combination of two non-mixing liquid $A$ and $B$ with its axis vertical. The densities of liquid $A$ and $B$ are $0.7$ $g/cm^3$ and $1.2$ $gm/cm^3$. The height of liquid $A$ is $h_A = 1.2$ $cm$ and the length of the part of cylinder immersed in liquid $B$ is $h_B = 0.8$ $cm$. Then the length part of the cylinder in air is ....... $cm$View Solution
- 5A tank is filled with water upto a height $1\,m$. A hole is made at a distance $20\, cm$ from top. Find, the horizontal distance from the base of the tank, where the water strikes the ground. ......... $cm$View Solution
- 6An object falling through a fluid is observed to have acceleration given by $a = g -bv$ where $g =$ gravitational acceleration and $b$ is constant. After a long time of release, it is observed to fall with constant speed. The value of constant speed isView Solution
- 7Determine the pressure difference in tube of non$-$uniform cross sectional area as shown in figure. $\Delta P =?$ (in $pa$)View Solution
$d_{1}=5\, cm , V_{1}=4\, cm , d_{2}=2\, cm , V_{2}=?$
- 8View SolutionA man is sitting in a boat which is floating in a pond. If the man drinks same water from the pond, the level of water in pond will
- 9Two water pipes $P$ and $Q$ having diameter $2 \times 10^{-2} \,m$ and $4 \times 10^{-2} \,m$ respectively are joined in series with the main supply line of water. The velocity of water flowing in pipe $P$ is ........View Solution
- 10A small drop of water falls from rest through a large height $h$ in air; the final velocity isView Solution