Viscosity and Stokes' law

If an air bubble of diameter 2 mm rises steadily through a liquid of density 2000 kg/m³ at a rate of 0.5 cm/s, then the coefficient of viscosity of liquid is ________ Poise. (Take $g=10$ m/s²)

A projectile of mass 200 g is launched in a viscous medium at an angle 60° with the horizontal, with an initial velocity of 270 m/s. It experiences a viscous drag force $\vec F = -c\vec v$ where the drag coefficient $c = 0.1$ kg/s and $\vec v$ is the instantaneous velocity of the projectile. The projectile hits a vertical wall after 2 s. Taking $e = 2.7$, the horizontal distance of the wall from the point of projection (in m) is _____.

A table tennis ball has radius $(3/2)\times10^{-2}\,\mathrm{m}$ and mass $(22/7)\times10^{-3}\,\mathrm{kg}$. It is slowly pushed down into a swimming pool to a depth of $d = 0.7\,\mathrm{m}$ below the water surface and then released from rest. It emerges from the water surface at speed $v$, without getting wet, and rises up to a height $H$. Which of the following option(s) is(are) correct?

[Given: $\pi = 22/7$, $g = 10\,\mathrm{m\,s^{-2}}$, density of water $= 1\times10^3\,\mathrm{kg\,m^{-3}}$, viscosity of water $= 1\times10^{-3}$ Pa-s.]

The terminal velocity ($v_t$) of the spherical rain drop depends on the radius (r) of the spherical rain drop as :

The velocity of upper layer of water in a river is $36\ \mathrm{kmh^{-1}}$. Shearing stress between horizontal layers of water is $10^{-3}\ \mathrm{Nm^{-2}}$. Depth of the river is ______ m. (Co-efficient of viscosity of water is $10^{-2}$ Pa.s)

If $\rho$ is the density and $\eta$ is coefficient of viscosity of fluid which flows with a speed $v$ in the pipe of diameter d, the correct formula for Reynolds number $R_e$ is :

Given below are two statements : One is labelled as Assertion A and the other is labelled as Reason R.

Assertion A : Product of Pressure (P) and time (t) has the same dimension as that of coeffcient of viscosity.

Reason R : Coefficient of viscosity $=\dfrac{\text{Force}}{\text{Velocity gradient}}$

Choose the correct answer from the options given below :

A water drop of radius 1 $\mu$m falls in a situation where the effect of buoyant force is negligible. Co-efficient of viscosity of air is $1.8\times10^{-5}$ Nsm$^{-2}$ and its density is negligible as compared to that of water $10^6$ gm$^{-3}$. Terminal velocity of the water drop is :

(Take acceleration due to gravity $=10$ ms$^{-2}$)

A small spherical ball of radius 0.1 mm and density $10^4$ kg m$^{-3}$ falls freely under gravity through a distance $h$ before entering a tank of water. If, after entering the water the velocity of ball does not change and it continue to fall with same constant velocity inside water, then the value of $h$ will be ______ m

(Given $g=10$ ms$^{-2}$, viscosity of water $=1.0\times10^{-5}$ N-sm$^{-2}$).

An air bubble of negligible weight having radius r rises steadily through a solution of density $\sigma$ at speed $v$. The coefficient of viscosity of the solution is given by :

The diameter of an air bubble which was initially 2 mm, rises steadily through a solution of density 1750 kg m$^{-3}$ at the rate of 0.35 cms$^{-1}$. The coefficient of viscosity of the solution is ______ poise (in nearest integer). (the density of air is negligible).

As shown schematically in the figure, two vessels contain water solutions (at temperature $T$) of potassium permanganate ($\ce{KMnO4}$) of different concentrations $n_1$ and $n_2\ (n_1 > n_2)$ molecules per unit volume with $\Delta n = (n_1 - n_2) \ll n_1$. When they are connected by a tube of small length $l$ and cross-sectional area $S$, $\ce{KMnO4}$ starts to diffuse from the left to the right vessel through the tube. Consider the collection of molecules to behave as dilute ideal gases and the difference in their partial pressure in the two vessels causing the diffusion. The speed $v$ of the molecules is limited by the viscous force $-\beta v$ on each molecule, where $\beta$ is a constant. Neglecting all terms of the order $(\Delta n)^2$, which of the following is/are correct? ($k_B$ is the Boltzmann constant)

Consider a thin square plate floating on a viscous liquid in a large tank. The height $h$ of the liquid in the tank is much less than the width of the tank. The floating plate is pulled horizontally with a constant velocity $u_0$. Which of the following statements is (are) true?

Two tubes of radii $r_1$ and $r_2$, and lengths $l_1$ and $l_2$, respectively, are connected in series and a liquid flows through each of them in stream line conditions. $P_1$ and $P_2$ are pressure differences across the two tubes. If $P_2$ is $4P_1$ and $l_2$ is $\dfrac{l_1}4$, then the radius $r_2$ will be equal to :

Consider two solid spheres P and Q each of density $8\ \mathrm{gm\,cm^{-3}}$ and diameters 1 cm and 0.5 cm, respectively. Sphere P is dropped into a liquid of density $0.8\ \mathrm{gm\,cm^{-3}}$ and viscosity $\eta=3$ poiseulles. Sphere Q is dropped into a liquid of density $1.6\ \mathrm{gm\,cm^{-3}}$ and viscosity $\eta=2$ poiseulles. The ratio of the terminal velocities of P and Q is

Which of the following option correctly describes the variation of the speed $v$ and acceleration '$a$' of a point mass falling vertically in a viscous medium that applies a force F = −kv, where 'k' is a constant, on the body ? (Graphs are schematic and not drawn to scale)

Two spheres $P$ and $Q$ of equal radii have densities $\rho_1$ and $\rho_2$, respectively. The spheres are connected by a massless string and placed in liquids $L_1$ and $L_2$ of densities $\sigma_1$ and $\sigma_2$ and viscosities $\eta_1$ and $\eta_2$, respectively. They float in equilibrium with the sphere $P$ in $L_1$ and sphere $Q$ in $L_2$ and the string being taut (see figure). If sphere $P$ alone in $L_2$ has terminal velocity $\vec V_P$ and $Q$ alone in $L_1$ has terminal velocity $\vec V_Q$, then

If it takes 5 minutes to fill a 15 litre bucket from a water tap of diameter $\dfrac2{\sqrt\pi}$ cm then the Reynolds number for the flow is (density of water = $10^3$ kg/m$^3$ and viscosity of water = $10^{-3}$ Pa.s) close to :

The amplitude of a simple pendulum, oscillating in air with a small spherical bob, decreases from 10 cm to 8 cm in 40 seconds. Assuming that Stokes law is valid, and ratio of the coefficient of viscosity of air to that of carbon dioxide is 1.3, the time in which amplitude of this pendulum will reduce from 10 cm to 5 cm in carbondioxide will be close to ($\ln5=1.601$, $\ln2=0.693$).

The velocity of water in a river is 18 km/hr near the surface. If the river is 5 m deep, find the shearing stress between the horizontal layers of water. The co-efficient of viscosity of water $=10^{-2}$ poise.