Question

A vertical tank, open at the top, is filled with a liquid and rests on a smooth horizontal surface. A small is opened at the centre of one side of the tank. The area of cross section of the tank is N times the area of the , where N is a large number. Neglect the mass of the tank itself. The initial acceleration of the tank is

(a) g/2N

(b) g/√2N

(c) g/N

(d) g/2√N

Answer 1

Correct Answer is: (c) g/N

v = √(2g. h/2) = √(g/h).

Let α be the area of the ****. The volume of the liquid discharged per unit time is vα.

The mass of the liquid discharged per unit time is ρvα.

The momentum of this liquid per unit time is ρv2α, which gives the force exerted by the liquid.

∴ F = ραv2 = ραgh.

The mass of the liquid in the tank is m = Ahρ.

Initial acceleration of the tank, F/m = αg/A = g/N.