Question

A cylinder containing water up to a height of $25\text{cm}$ has a hole of cross section $\frac{1}{4}{\text{cm}}^2$ in its bottom. It is counter poised in a balance. What is the initial change in the balancing weight when the water begins to flow

• A. Increases of 12.5 g-wt
• B. Increases of 6.25 g-wt
• C. Decrease of 12.5 g-wt
• D. Decrease of 6.25 g-wt

Answer 1

The correct option is C Decrease of 12.5 g-wt

Let
$A=$ area of cross section of hole
$V=$ initial velocity
$d=$ density of water
Initial mass of water flowing out per second = $dAV$
Rate of change of momentum = $A{V}^{2}d$
Initial upward reaction $=Ad{V}^2$
$V=\sqrt{2gh}$
$\therefore$ Decrease in weight $=Ad\left(2gh\right)$ $=2Adgh$
$2\times |\frac{1}{4}|\times \frac{1}{1000}\times 980\times 25=12.25kg-cm/s^2=0.1225N$
$=\frac{0.1225}{9.8}kg-wt=12.5g-wt$