A small ball of mass $M$ and density $\rho$ is dropped in a viscous liquid of density $\rho_0$. After some time, the ball falls with a constant velocity. What is the viscous force on the ball ?
JEE MAIN 2023, Medium
Download our app for free and get started
For constant velocity $F_{\text {net }}=0$
$\mathrm{F}_{\mathrm{vis}}+\rho_0 \mathrm{vg}=\rho \mathrm{vg}$
$\mathrm{F}_{\mathrm{vis}}=\left(\rho-\rho_0\right) \mathrm{vg}$
$=\rho \mathrm{vg}\left(1-\frac{\rho_0}{\rho}\right)$
$=\mathrm{Mg}\left(1-\frac{\rho_0}{\rho}\right)$
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
- 1A hollow sphere of volume $V$ is floating on water surface with half immersed in it. What should be the minimum volume of water poured inside the sphere so that the sphere now sinks into the waterView Solution
- 2Two capillary tubes of the same length but different radii $r_1 $ and $r_2$ are fitted in parallel to the bottom of a vessel. The pressure head is $ P. $ What should be the radius of a single tube that can replace the two tubes so that the rate of flow is same as beforeView Solution
- 3A 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
- 4View SolutionA viscous fluid is flowing through a cylindrical tube. The velocity distribution of the fluid is best represented by the diagram
- 5A air bubble rises from bottom of a lake to surface. If its radius increases by $200 \%$ and atmospheric pressure is equal to water coloumn of height $H$. then depth of lake is ..... $H$View Solution
- 6A spray gun is shown in the figure where a piston pushes air out of a nozzle. A thin tube of uniform cross section is connected to the nozzle. The other end of the tube is in a small liquid container. As the piston pushes air through the nozzle, the liquid from the container rises into the nozzle and is sprayed out. For the spray gun shown, the radii of the piston and the nozzle are $20 \ mm$ and $1 \ mm$ respectively. The upper end of the container is open to the atmosphere. $Image$View Solution
$1.$ If the piston is pushed at a speed of $5 \ mms ^{-1}$, the air comes out of the nozzle with a speed of
$(A)$ $0.1 \ ms ^{-1}$ $(B)$ $1 \ ms ^{-1}$ $(C)$ $2 \ ms ^{-1}$ $(D)$ $8 \ ms ^{-1}$
$2.$ If the density of air is $\rho_{ a }$ and that of the liquid $\rho_{\ell}$, then for a given piston speed the rate (volume per unit time) at which the liquid is sprayed will be proportional to
$(A)$ $\sqrt{\frac{\rho_{ a }}{\rho_{\ell}}}$ $(B)$ $\sqrt{\rho_a \rho_{\ell}}$ $(C)$ $\sqrt{\frac{\rho_{\ell}}{\rho_{ a }}}$ $(D)$ $\rho_{\ell}$
Give the answer question $1$ and $2.$
- 7A large tank is filled with water (density $=$ $10^3 $ $kg/m^3$).A small hole is made at a depth $10$ $m$ below water surface. The range of water issuing out of the hole is Ron ground. What extra pressure must be applied on the water surface so that the range becomes $2R $ (take $1$ $atm$ $=$ $10^5$ $Pa$ and $g$ $=$ $10$ $m/s^2):$ ...... $atm$View Solution
- 8Different heads are in Column - $\mathrm{I}$ and its formulas are given in Column - $\mathrm{II}$. Match them appropriately.View Solution
Column - $\mathrm{I}$ Column - $\mathrm{II}$ $(a)$ Velocity head $(i)$ $\frac{P}{{\rho g}}$ $(b)$ Pressure head $(ii)$ $h$ $(iii)$ $\frac{{{v^2}}}{{2g}}$ - 9The 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
- 10View SolutionAn application of Bernoulli's equation for fluid flow is found in