A vessel with a symmetrical hole in its bottom is Paste on a cart. The mass of the vessel and the cart is `1.5 kg`. With what force `F` (in `xx 10^(2)N)` should the cart be pulled that the maximum amount of water remains in the vessel. The dimensions of the vessel are as shown in the figure. Given that `b = 50 cm, c = 10 cm`, area of base `A= 40cm^(2), L = 20 cm, g = 10 m//s^(2).

Answer

1

Explanation

As the cart is drawn by a force `F`, the water in the vessel takes up a slant position rising upward at the back wall of the vesel. To prevent water flowing out of the hole `H`, the acceleration of the vessel should have such a value it occupies a face area `DBH` and a width of vessel given by `A.L`.
Area of `/_\DBH=1/2bc`
Volume of liquid retained `=1/2bcxxA/L`
Mass of cart and water `=M+(bcArho)/(2L)`
`tantheta=(ma)/(mg`
`a=gtantheta=gxxb/c`
Required force `(M+(bcAr)/(2L)(gb)/c)=[1.5+0.5]xx50=2.0xx50=100N`