Question

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

• A. Increase of 12.5 gm - wt
• B. Increase of 6.25 gm - wt
• C. Decrease of 12.5 gm - wt
• D. Decrease of 6.25 gm - wt

Answer 1

The correct option is C Decrease of 12.5 gm - wt

Let A = The area of cross section of the hole, v =
Initial velocity of efflux, d = Density of water,
Initial volume of water flowing out per second = Av Initial mass of water flowing out per second = Avd
Rate of change of momentum = $Ad{v}_2\therefore$ Initial downward force on the out flowing water =$Ad{v}_2$
So equal amount of reaction acts upwards on the cylinder. $\therefore$ Initial upward reaction = $Ad{v}_2$ $[Asv=\sqrt{2gh}]$
$\therefore$ Initial decrease in weight = $Ad\left(2gh\right)=2Adgh=2\times \left(\frac{1}{4}\right)\times 1\times 980\times 25=12.5gm-wt.$