Question

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 initial change in the balancing weight when water begin 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

Correct Answer - C
Let A = The area of cross section of the hole, `upsilon` = Initial velocity of efflux, d = Density of water,
Initial mass of water flowing out per second = `Aupsilon`
Initial mass of water flowing out per second = `Aupsilond`
Rate of change of momentum `= Adupsilon^(2)" " therefore` Initial downward force on the out flowing water `=Adupsilon^(2)`
So equal amount of reaction acts upwards on the cylinder.
`therefore` Initial upward reaction `=Adv^(2) " " [As v =sqrt(2gh)]`
`therefore` Initial decrease in weight `=Ad (2gh) = 2Adgh = 2xx((1)/(4))xx1xx980xx25 = 12.5 gm-wt`.