A cylinder containing water up to a height of `25cm` has a hole of cross-section `1/4 cm^(2)` in its bottom. It is counterpoised in a balance. What is the intial change in the balancing weight when water begin to flow up?

Options

A. increases of `12.5 gwt`
B. increase of `6.25 gwt`
C. Decrease of `12.5 gwt`
D. Decrease of `6.25 gwt`

Answer

C

Explanation

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 actys upwards on the cylinder.
`:. I nitial upward reaction = `Adv^(2) [As v = sqrt(2gh)]`
`:. i nital decrease in weight = Ad(2gh)`
`=2Adgh = 2 xx (1/4)xx1xx980xx25=12.5 gm-wt`.