Question

A cylinder containing water up to a height of $24cm$ has a hole in its bottom. It is counter-poised in a balance. When water begins to flow out, the initial decrease in balancing weight is required to be $12gf$ to keep the balance beam horizontal. The cross-sectional area of the hole is :

• A. $0.12c{m}^2$
• B. $0.25c{m}^2$
• C. $0.50c{m}^2$
• D. $0.75c{m}^2$

Answer 1

Answer: (B)

$0.25c{m}^2$

From Toricellis theorem $v=\sqrt{2gh}$

So, force exerted by the let of liquid on cylinder $=fa{v}^2$ ...........(1) [where a is cross sectional area]

Decrease in balancing weight $=2gh$.............(2)

So, in order to balance,

$\left(1\right)=\left(2\right)$

$\lambda a,2g\times 24=12\times g$$\Rightarrow a=\frac{12}{2\times 24}c{m}^2$$\Rightarrow a=0.25c{m}^2$