Question

A plate of area 100 $c{m}^2$ is placed on the upper surface of castor oil, 2 mm thick. Taking the coefficient of viscosity to be 15.5 poise , calculate the horizontal force necessary to move the plate with a velocity 3 cm $s^{-1}.$

• A. 0.28 N
• B. 0.2455 N
• C. 0.2325 N
• D. 0.1 N

Answer 1

Answer: (C)

0.2325 N

Area $A=100㎠=100\times {10}^{-4}㎡$

Thickness $dx=2㎜=2\times {10}^{-3}m$

Co efficient of viscosity$=15.5$ poise$=1.55$pa

Velocity$=3㎝s^{-1}=3\times {10}^{-2}㎧$

$F=\eta A\left(\frac{dv}{dx}\right)$

$=\frac{15.5\times {10}^{-1}\times 100\times 3\times {10}^{-4}\times {10}^{-2}}{2\times {10}^{-3}}$

$=\frac{23.25\times {10}^{-7}}{{10}^{-5}}$

$F=0.2325N$