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

detailed solution

Correct option is C

Let A = The area of cross section of the hole v = Initial velocity of effluxd = Density of water, Initial volume of water flowing out per second = AvInitial mass of water flowing out per second = AvdRate of change of momentum = Adv2     Initial downward force on the flowing out water = Adv2So equal amount of reaction acts upwards on the cylinder.  ∴ Initial upward reaction = Adv2   [As  v=2gh ]∴ Initial decrease in weight  =Ad (2gh)=2 Adgh =2×14×1×980×25=12.5 gm-wt.