A plastic circular disc of radius R is placed on a thin oil film, spread over a flat horiz

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9-1.Fluid Mechanics

hard

A plastic circular disc of radius $R$ is placed on a thin oil film, spread over a flat horizontal surface. The torque required to spin the disc about its central vertical axis with a constant angular velocity is proportional to

$R^2$

$R^3$

$R^4$

$R^6$

Solution

Let coefficient of viscosity $\&$ thickness of film

$\rightarrow \eta \&$ x respectively

Viscous force on element ring is

$\mathrm{dF}=\eta(2 \pi \mathrm{rdr})\left[\frac{\mathrm{wr}-0}{\mathrm{x}}\right]$

$\mathrm{d} \tau=(\mathrm{dF}) r$

$\therefore \tau=\frac{\eta 2 \pi \mathrm{w}}{\mathrm{t}} \int_{0}^{\mathrm{R}} \mathrm{r}^{3} \cdot \mathrm{dr}=\left(\frac{\eta(2 \pi) \mathrm{w}}{4 \mathrm{x}}\right) \mathrm{R}^{4}$

$\therefore \tau \propto R^{4}$

Standard 11

Physics

The terminal velocity of a copper ball of radius $2.0 \;mm$ falling through a tank of oll at $20\,^{\circ} C$ is $6.5 \;cm s ^{-1} .$ Compute the viscosity of the oil at $20\,^{\circ} C .$ Density of oil is $1.5 \times 10^{3} \;kg m ^{-3},$ density of copper is $8.9 \times 10^{3} \;kg m ^{-3}$

easy

An air bubble of $1\, cm$ radius is rising at a steady rate of $2.00\, mm/sec$ through a liquid of density $1.5\, gm$ per $cm^3$. Neglect density of air. If $g$ is $1000\, cm/sec^2$, then the coefficient of viscosity of the liquid is

medium

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)

medium

(JEE MAIN-2016)

Write the equation of terminal velocity.

easy

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 :

easy

(NEET-2022)

A plastic circular disc of radius $R$ is placed on a thin oil film, spread over a flat horizontal surface. The torque required to spin the disc about its central vertical axis with a constant angular velocity is proportional to

Solution

Similar Questions

The terminal velocity of a copper ball of radius $2.0 \;mm$ falling through a tank of oll at $20\,^{\circ} C$ is $6.5 \;cm s ^{-1} .$ Compute the viscosity of the oil at $20\,^{\circ} C .$ Density of oil is $1.5 \times 10^{3} \;kg m ^{-3},$ density of copper is $8.9 \times 10^{3} \;kg m ^{-3}$

An air bubble of $1\, cm$ radius is rising at a steady rate of $2.00\, mm/sec$ through a liquid of density $1.5\, gm$ per $cm^3$. Neglect density of air. If $g$ is $1000\, cm/sec^2$, then the coefficient of viscosity of the liquid 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)

Write the equation of terminal velocity.

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 :

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