A cylindrical tank having cross-sectional area `A = 0.5 m^(2)` is filled with two liquids of density `rho_(1)=900 kg m^(-3)` and `rho_(2)=600 kgm^(-3)`, to a height `h=60cm` each as shown in the figure. A small hole having area `a=5cm^(2)` is made in right vertical wall at a height `y = 20 cm` from the bottom. A horizontal force `F` is applied on the tank to keep it in static equilibrium. The tank is lying on a horizontal surface. Neglect mass of the cylindrical tank in comparison to mass of the liquids (`ake g = 10 ms^(-2)`).

(i) horizontal force F to keep the cylinder in static equilibrium, if it is placed on a smooth horizontal plane and (ii) minimum and maximum values of F to keep the cylinder in static equilibrium, if coefficient of friction between the cylinder and the plane is µ = 0.01. (g = 10 ms –2 )

Options

A. `0,40N`
B. `5.4N,52.2N`
C. `0,70N`
D. `0,52.2N`

Answer

D

Explanation

Total mass of the liquid on the cylinder is
`m=Ahrho_(1)+Ahrho_(2)=450kg`
Limiting friction `= mumg=45N`
Since `Flt` limiting friction, thereforce minimum force required is zoro. Considering the free body diagram for maximum vertical forces.
`N=mg`
Now considering the horizontal forces
`F_("max")=F+muN=52.2N`