Question

A metal plate $10cm$ square rests on a $2mm$ thick caster oil layer. Calculate the horizontal force needed to move the plate with speed $3cm$ $s^{-1}$ (Coefficient of viscosity of caster oil is $15$ poise.)

• A. $2.25\times {10}^{-2}$
• B. $2.25\times {10}^{-1}$
• C. $2.25\times {10}^{-3}$
• D. $2.25\times {10}^{-4}$

Answer 1

The correct option is A $2.25\times {10}^{-2}$

Horizontal force needed to move is given by

$F=\eta A\frac{dv}{dx}$

where $A={10}^{-2}{m}^2$ , $dx=2\times {10}^{-3}m$

$dv=3\times {10}^{-2}m/s$ and $\eta =15\times {10}^{-1}Pa/s$

Putting values we get

$F=15\times {10}^{-1}\times {10}^{-2}\times \frac{3\times {10}^{-2}}{2\times {10}^{-3}}=2.25\times {10}^{-2}N$

Option A is correct