Properties Of Solids And Liquids Question 198

Question: A cylinder containing water up to a height of 25 cm has a hole of cross-section $ \frac{1}{4}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

Options:

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

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Answer:

Correct Answer: C

Solution:

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 = Adv2 Initial downward force on the flowing out water = Adv2 So equal amount of reaction acts upwards on the cylinder.

Initial upward reaction =$ Adv^{2} $

[As $ v=\sqrt{2gh} $ ]

$ \therefore $ 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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