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

Text Solution
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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 = Adv 2
Initial downward force on the flowing out water = Adv 2 So equal amount of reaction acts upwards on the cylinder.
∴ ∴ Initial upward reaction = $\mathrm{Adv}^2$ [As $v = \sqrt{2gh}$ ]
Initial decrease in weight = Ad(2gh)
= 2Adgh $= 2 \times \left( \frac{1}{4} \right) \times 1 \times 980 \times 25 = 12.5$ gm-wt.
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