$($a$)$ A circular plate is pulled by a force $($F$)$ as shown in Fig. B$\mathrm{.}5$a$.$ The clearances of $5mm$ and $4mm$ between the circular plate and the fluid container are filled with two different oils with different kinematic viscosity $(v)$ in the ratio of $1$:$4.$ The kinematic viscosity of the top oil is $500{10}^{-6}\frac{m^2}{s}.$ Both the specific gravity of top oil and bottom oil are $0\mathrm{.}89.$

$($i$)$ Show that the force $($F$)$ required to pull the circular plate is the diameter of the circular plate, and $L$ is the leng

$\frac{4}{9}$

circular plate.

$($s

$($ii$)$ If the force required is $100N,$ the diameter of the circular plate is $0\mathrm{.}4m,$ and the length of the circular plate is $2m,$ calculate the required velocity $(u).$

$(2$ marks$)$

Fig. B$\mathrm{.}5$a