Question

An open cylinderical container of negligible mass has cross–sectional area A. There is a small hole at the bottom having cross-sectional area 1% of the cylinder. The cylinder is placed on a smooth horizontal surface. The cylinder is filled with a liquid of density ρ . The mass of liquid in cylinder is M. At t = 0 the hole is opened. The intial acceleration of cylinder is

(1) zero

(2) g

(3) g x 10^-1

(4) 2g x 10^-2

Answer 1

(4) 2g x 10^-2

Let H be the initial height of liquid in cylinder. Clearly

Let v₀ be the initial velocity of efflux of liquid through hole. From Bernoulli’s principle

Let a be area of cross–section of hole. Given a A/100 . Let F₀ be the initial force on cylinder due to liquid flowing out from O.

The initial acceleration of cylinder