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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` |
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Answer» 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`. |
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