A $20 \,cm$ long tube is closed at one end. It is held vertically, and its open end is dipped in water until only half of it is outside the water surface. Consequently, water rises in it by height $h$ as shown in the figure. The value of $h$ is closest to .............. $\,m / s$ (assume that the temperature remains constant, $P _{\text {armosphere }}=10^5 \,N / m ^2$, density. of water $=10^3 \,kg / m ^3$, and acceleration due to gravity $g =10 \,m / s ^2$ )
KVPY 2021, Advanced
Download our app for free and get started
(D)
Let final pressure inside tube be $P$
Apply $P_1 V_1=P_2 V_2$
$10^5 \times 20= P \times(20- h ) \ldots(1)$
Pressure Equation
$P = P _0+\rho g \frac{(10- h )}{100}$
$P =10^5+10^3 \times 10 \times \frac{(10- h )}{100}$
$P =10^5\left(1+\frac{10- h }{10^3}\right) \ldots(2)$
Substitute $(2)$ in $(1)$
$10^5 \times 20=10^5\left(1+\frac{10-h}{10^3}\right)(20- h )$
Solve for $h$
$h =0.2 \,cm$
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
- 1Asphere of radius $R$ and made of material of relative density $\sigma$ has a concentric cavity of radius $r$. It just floats when placed in a tank full of water. The value of the ratio $R/r$ will beView Solution
- 2An object suspended by a wire stretches it by $10 \,mm$. When object is immersed in a liquid the elongation in wire reduces by $\frac{10}{3} \,mm$. The ratio of relative densities of the object and liquid is ............View Solution
- 3The volume of an air bubble is doubled as it rises from the bottom of lake to its surface. The atmospheric pressure is $75 \,cm$ of mercury. The ratio of density of mercury to that of lake water is $\frac{40}{3}$. The depth of the lake in metre is .........View Solution
- 4A hemispherical bowl just floats without sinking in a liquid of density $1.2 × 10^3kg/m^3$. If outer diameter and the density of the bowl are $1 m$ and $2 × 10^4 kg/m^3$ respectively, then the inner diameter of the bowl will be........ $m$View Solution
- 5View SolutionThe Working of an atomizer depends upon
- 6A tiny spherical oil drop carrying a net charge $q$ is balanced in still air with a vertical uniform electric field of strength $\frac{81 \pi}{7} \times 10^5 \mathrm{Vm}^{-1}$. When the field is switched off, the drop is observed to fall with terminal velocity $2 \times 10^{-3} \mathrm{~ms}^{-1}$. Given $\mathrm{g}=9.8 \mathrm{~ms}^{-2}$, viscosity of the air $=1.8 \times 10^{-5} \mathrm{Ns} \mathrm{m}^{-2}$ and the density of oil $=$ $900 \mathrm{~kg} \mathrm{~m}^{-3}$, the magnitude of $\mathrm{q}$ isView Solution
- 7An aeroplane of mass $3 \times 10^4\,kg$ and total wing area of $120\,m^2$ is in a level flight at some height. The difference in pressure between the upper and lower surfaces of its wings in kilopascals is........... $kPa$ $(g=10\,m/s^2)$View Solution
- 8A jet of water with cross section of $6$ $cm^2$ strikes a wall at an angle of $60^o $ to the normal and rebounds elastically from the wall without losing energy. If the velocity of the water in the jet is $12$ $m/s$, the force acting on the wall is ....... $N$View Solution
- 9Different physical quantities are given in Column - $\mathrm{I}$ and their dimensional formula are given in Column - $\mathrm{II}$. Match them appropriately.View Solution
Column - $\mathrm{I}$ Column - $\mathrm{II}$ $(a)$ Viscous force $(i)$ $\left[ {{M^1}{L^1}{T^{ - 2}}} \right]$ $(b)$ Coefficient of viscosity $(ii)$ $\left[ {{M^1}{L^{ - 1}}{T^{ - 1}}} \right]$ $(iii)$ $\left[ {{M^1}{L^{ - 1}}{T^{ - 2}}} \right]$ - 10A liquid is kept in a cylindrical vessel which is being rotated about a vertical axis through the centre of the circular base. If the radius of the vessel is $ r $ and angular velocity of rotation is $\omega $, then the difference in the heights of the liquid at the centre of the vessel and the edge isView Solution