Question

A horizontal force of 1 N is required to move a metal plate of area $\sf 10^{-2}$ m² with a velocity of $\sf 2 \times 10^{-2}$ m/s, when it rests on a layer of oil $\sf 1.5 \times 10^{-3}$ m thick. Find the coefficient of viscosity of oil.​

Answer 1

Answer

• Coefficient of viscosity of oil = 7.5

Given

• A horizontal force of 1 N is required to move a metal plate of area  10⁻² m² with a velocity of  2 * 10⁻² m/s, when it rests on a layer of oil  1.5 * 10⁻³ m thick

To Find

• Coefficient of viscosity of oil

Formula Used

$\bf F=\eta A\dfrac{dv}{dx}$

where ,

F denotes force

η denotes coefficient of viscosity

A denotes area

dv denotes velocity

dx denotes thickness

Solution

$\bf F=\eta A\dfrac{dv}{dx}\\\\\implies 1=\eta \times 10^{-2}\times \dfrac{2 \times 10^{-2}}{1.5 \times 10^{-3}}\\\\ \implies \bf \eta = \dfrac{1.5 \times 10^{-3}}{2 \times 10^{-4}}\\\\\implies \bf \eta = \dfrac{1.5 \times 10}{2}\\\\\implies \bf \eta =\dfrac{15}{2}\\\\\implies \bf \eta =7.5$

So , Coefficient of viscosity of oil , η = 7.5

Answer 2

GiveN :

• Force (F) = 1 N
• Area (A) = $\sf{10^{-2} \: m^2}$
• Velocity (V) = $\sf{2 \: \times \: 10^{-2} \: ms^{-1}}$
• Thickness (x) = $\sf{1.5 \: \times \: 10^{-3} \: m}$

To FinD :

• Coefficient of Viscosity $\sf{(\eta)}$

SolutioN :

Use Newton's Law of Viscosity :

$\longrightarrow {\boxed{\sf{F \: = \: \eta A \dfrac{dv}{dx}}}} \\ \\ \longrightarrow \sf{1 \: = \: \eta \: \times \: 10^{-2} \bigg\lgroup \dfrac{2 \: \times \: 10^{-2}}{1.5 \: \times \: 10^{-3}} \bigg\rgroup} \\ \\ \longrightarrow \sf{1 \: = \: \eta \: \times \: 10^{-2} \bigg( 1.33 \: \times \: 10^{-2 \: + \: 3} \bigg)} \\ \\ \longrightarrow \sf{1 \: = \: \eta \: \times \: 10^{-2} \: \times \: 1.33 \: \times \: 10^1} \\ \\ \longrightarrow \sf{1 \: = \: \eta \: \times \: 1.33 \: \times \: 10^{-2 \: + \: 1}} \\ \\ \longrightarrow \sf{1 \: = \: \eta \: \times \: 1.33 \: \times \: 10^{-1}} \\ \\ \longrightarrow \sf{\eta \: = \: \dfrac{1}{1.33 \: \times \: 10^{-1}}} \\ \\ \longrightarrow \sf{\eta \: = \: 0.75 \: \times \: 10} \\ \\ \longrightarrow \sf{\eta \: = \: 7.5 \: poise \: (approx.)}$