Question

Find the minimum force required to drag a hard polythene plate of area 2 $m^2$ on a thin film of oil of thickness 0.25 cm and $\eta$ = 15 poise. Assume the speed of the plate is 10 cm $s^{-1}.$

• A. $F=5.2\times {10}^{7}dyne$
• B. $F=4.2\times {10}^{7}dyne$
• C. $F=3.2\times {10}^{7}dyne$
• D. $F=1.2\times {10}^{7}dyne$

Answer 1

Answer: (D)

$F=1.2\times {10}^{7}dyne$

Area of plate$=2㎡$

Thickness of film$=0.25㎝=0.25\times {10}^{-2}m$

$\eta =1.5$ poise$=1.5$Pa

Speed of plate$=10㎝s^{-1}=10\times {10}^{-2}m{s}^{-1}$

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

$=\frac{1.5\times 2\times 10\times {10}^{-2}}{0.25\times {10}^{-2}}N=120N$

$F=1.2\times {10}^7$