First slide

Viscosity

Question

A cube having length of side 10 cm and made of a material of density 4 gm/cm³, is projected horizontally with a velocity of 4 m/s on a horizontal surface. There is a thin film off grease of thickness 0.2 mm between the cube and the horizontal surface. If the cube stops after travelling a distance of 10 m, the viscosity of grease in N-S/m² is

Moderate

A

0.016
B

0.024
C

0.084
D

0.054

Solution

Viscous drag $F_{D} = A . η . \frac{V}{t} = l^{2} . η . \frac{V}{t}$
Deceleration, $a = \frac{F_{D}}{m} = \frac{l^{2} . η . \frac{V}{t}}{l^{3} ρ} = \frac{ηV}{ρlt}$
Now $V^{2} - 2 a . S = 0 \Rightarrow V^{2} = 2 . \frac{ηV}{ρlt} . S$
$\Rightarrow η = \frac{ρVlt}{2 S} = \frac{4000 \times 4 \times 0 .1 \times 0 .2 \times 10^{- 3}}{2 \times 10} \frac{N - S}{m^{2}}$
$\Rightarrow η = 0 .016 N - S / m^{2}$

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