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
Show Answer
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.
