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 " kg "m^(-3)` , to a height a ` = 6 cm^(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 surfaces . Neglect mass of cylindrical tank camparison to mass of liquids ( take ` g = 10 ms^(-2)`)

Minimum and maximum values of F to keep the cylinder in static just after the water starts to spill through the hole . If the co - efficient of static friction between contact surfaces is `0.01`

Options

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

Explanation

Total mass of the liquid in the cylinder is
` m = A hrho_(1) +A h rho_(2) = 450 Kg`
Limiting friction ` = mumg = 45 N `
` :. F lt ` limiting friction , therefore , minimum force required is zero .
Consider free body diagram for mximum vertical froces .
N = mg
Now considering horizontal forces ,
N = mg
` F_(max) = F+ muN `
or `F_(max) = 52.2 N `