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Q)

A metal plate of cross-sectional area rests on a layer of caster oil $(\eta= 15.5 p) \;0.2\;cm$ thick. Calculate the horizontal force required to move the plate with a speed of $3 cm/s$

\[\begin {array} {1 1} (a)\;1.213\;N \\ (b)\;0.233\;N \\ (c)\;2.33\;N \\ (d)\;5.133\;N \end {array}\]

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A)
$F=- \eta A \large\frac{dv}{dx}$
When $\eta=15.5\;p\qquad A=100\;cm^2$
$\large\frac{dv}{dx}=\frac{3}{0.2}$$=15 s^{-1}$
$F=-15.5 \times 100 \times 15$
$\qquad= -23250\; dynes$
$\qquad= -0.233 N$
force required $=0.233\;N$
Hence b is the correct answer.

 

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