A 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 $\mathrm{q}$ is
A 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 $\mathrm{q}$ is
- [IIT 2010]
- A
$1.6 \times 10^{-19} \mathrm{C}$
- B
$3.2 \times 10^{-19} \mathrm{C}$
- C
$4.8 \times 10^{-19} \mathrm{C}$
- D
$8.0 \times 10^{-19} \mathrm{C}$
Similar Questions
As shown schematically in the figure, two vessels contain water solutions (at temperature $T$ ) of potassium permanganate $\left( KMnO _4\right)$ of different concentrations $n_1$ and $n_2\left(n_1>n_2\right)$ molecules per unit volume with $\Delta n=\left(n_1-n_2\right) \ll n_1$. When they are connected by a tube of small length $\ell$ and cross-sectional area $S , KMnO _4$ 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)-
$(A)$ the force causing the molecules to move across the tube is $\Delta n k_B T S$
$(B)$ force balance implies $n_1 \beta v \ell=\Delta n k_B T$
$(C)$ total number of molecules going across the tube per sec is $\left(\frac{\Delta n}{\ell}\right)\left(\frac{k_B T}{\beta}\right) S$
$(D)$ rate of molecules getting transferred through the tube does not change with time
As shown schematically in the figure, two vessels contain water solutions (at temperature $T$ ) of potassium permanganate $\left( KMnO _4\right)$ of different concentrations $n_1$ and $n_2\left(n_1>n_2\right)$ molecules per unit volume with $\Delta n=\left(n_1-n_2\right) \ll n_1$. When they are connected by a tube of small length $\ell$ and cross-sectional area $S , KMnO _4$ 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)-
$(A)$ the force causing the molecules to move across the tube is $\Delta n k_B T S$
$(B)$ force balance implies $n_1 \beta v \ell=\Delta n k_B T$
$(C)$ total number of molecules going across the tube per sec is $\left(\frac{\Delta n}{\ell}\right)\left(\frac{k_B T}{\beta}\right) S$
$(D)$ rate of molecules getting transferred through the tube does not change with time
- [IIT 2020]
A solid sphere, of radius $R$ acquires a terminal velocity $\nu_1 $ when falling (due to gravity) through a viscous fluid having a coefficient of viscosity $\eta $. The sphere is broken into $27$ identical solid spheres. If each of these spheres acquires a terminal velocity, $\nu_2$, when falling through the same fluid, the ratio $(\nu_1/\nu_2)$ equals
A solid sphere, of radius $R$ acquires a terminal velocity $\nu_1 $ when falling (due to gravity) through a viscous fluid having a coefficient of viscosity $\eta $. The sphere is broken into $27$ identical solid spheres. If each of these spheres acquires a terminal velocity, $\nu_2$, when falling through the same fluid, the ratio $(\nu_1/\nu_2)$ equals
- [JEE MAIN 2019]
The terminal velocity of a copper ball of radius $5\,mm$ falling through a tank of oil at room temperature is $10\,cm\,s ^{-1}$. If the viscosity of oil at room temperature is $0.9\,kg\,m ^{-1} s ^{-1}$, the viscous drag force is :
The terminal velocity of a copper ball of radius $5\,mm$ falling through a tank of oil at room temperature is $10\,cm\,s ^{-1}$. If the viscosity of oil at room temperature is $0.9\,kg\,m ^{-1} s ^{-1}$, the viscous drag force is :
- [NEET 2022]
Assume that, the drag force on a football depends only on the density of the air, velocity of the ball and the cross-sectional area of the ball. Balls of different sizes but the same density are dropped in an air column. The terminal velocity reached by balls of masses $250 \,g$ and $125 \,g$ are in the ratio
Assume that, the drag force on a football depends only on the density of the air, velocity of the ball and the cross-sectional area of the ball. Balls of different sizes but the same density are dropped in an air column. The terminal velocity reached by balls of masses $250 \,g$ and $125 \,g$ are in the ratio
- [KVPY 2018]
Write $\mathrm{SI}$ and $\mathrm{CGS}$ unit of coefficient of viscosity.
Write $\mathrm{SI}$ and $\mathrm{CGS}$ unit of coefficient of viscosity.