First slide

Viscosity

Question

A cube, made of a material of density 6 gm/cm³ and having length of each side 20 cm is sliding down an inclined surface having inclination 30^o with horizontal with a velocity of 5 m/s on a layer of grease of thickness 0.2 mm. Then coefficient of viscosity of grease is

Moderate

A

0.84 $\frac{N - S}{m^{2}}$
B

0.08 $\frac{N - S}{m^{2}}$
C

0.12 $\frac{N - S}{m^{2}}$
D

0.24 $\frac{N - S}{m^{2}}$

Solution

Viscous drag, $F_{D} = A . (η \frac{V}{t}) = l^{2} \times (η \frac{V}{t})$
Since net force on the cube is zero, we can write, $l^{2} \times \frac{ηV}{t} = mg \sin 30^{o} \Rightarrow \frac{l^{2} ηV}{t} = l^{3} ρ . g . \frac{1}{2} \Rightarrow η = \frac{ρlgt}{2 V}$
$\Rightarrow η = - \frac{6000 \times 0 .2 \times 10 \times 0 .2 \times 10^{- 3}}{2 \times 5} \frac{N - S}{m^{2}} = 0 .24 \frac{N - S}{m^{2}}$

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