A thin square plate of side $2\ m$ is moving at the interface of two very viscous liquids of viscosities ${\eta _1} = 1$ poise and ${\eta _2} = 4$ poise respectively as shown in the figure. Assume a linear velocity distribution in each fluid. The liquids are contained between two fixed plates. $h_1 + h_2 = 3\ m$ . A force $F$ is required to move the square plate with uniform velocity $10\ m/s$ horizontally then the value of minimum applied force will be ........ $N$

817-734

  • A

    $6$

  • B

    $12$

  • C

    $24$

  • D

    $40$

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  • [JEE MAIN 2024]

There is a $1\, mm$ thick layer of glycerine between a flat plate of area $100\, cm^2$ and a big plate. If the coefficient of viscosity of glycerine is $1.0\, kg\, (m-s)$, then ....... $N$ force is required to move the plate with a velocity of $7\, cm/s$ .