{"id":250534,"date":"2022-09-10T10:29:30","date_gmt":"2022-09-10T04:59:30","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/question\/water-is-filled-in-a-cylindrical-container-to-a-height-of-3m-the-ratio-of-the-cross-sectional-area-of-the-orifice-and-the-beaker-is-0-1-the-square-of-the-speed-of-the-liquid-coming-out-from-the-orif\/"},"modified":"2022-09-10T10:29:30","modified_gmt":"2022-09-10T04:59:30","slug":"water-is-filled-in-a-cylindrical-container-to-a-height-of-3m-the-ratio-of-the-cross-sectional-area-of-the-orifice-and-the-beaker-is-0-1-the-square-of-the-speed-of-the-liquid-coming-out-from-the-orif","status":"publish","type":"questions","link":"https:\/\/infinitylearn.com\/surge\/question\/physics\/water-is-filled-in-a-cylindrical-container-to-a-height-of-3m\/","title":{"rendered":"Water is filled in a cylindrical container to a height of 3m. The ratio of the cross-sectional area of the orifice and the beaker is 0.1. The square of the speed of the liquid coming out from the orifice is (g = l0\u00a0m\/s2)\u00a0"},"content":{"rendered":"","protected":false},"author":1,"template":"","meta":{"_yoast_wpseo_focuskw":"","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"Water is filled in a cylindrical container to a height of 3m. The ratio of the cross-sectional area of the orifice and the beaker is 0.1. The square of the speed of the liquid coming out from the orifice is (g = l0\u00a0m\/s2)\u00a0","custom_permalink":"question\/physics\/water-is-filled-in-a-cylindrical-container-to-a-height-of-3m\/"},"categories":[],"acf":{"question":"

Water is filled in a cylindrical container to a height of 3m. The ratio of the cross-sectional area of the orifice and the beaker is 0.1. The square of the speed of the liquid coming out from the orifice is (g = l0 m<\/mi>\/<\/mo>s<\/mi>2<\/mn><\/msup><\/math>)<\/p>
<\/figure>

 <\/p>","options":[{"option":"

50 m<\/mi>2<\/mn><\/msup>\/<\/mo>s<\/mi>2<\/mn><\/msup><\/math><\/p>","correct":true},{"option":"

50.5 m<\/mi>2<\/mn><\/msup>\/<\/mo>s<\/mi>2<\/mn><\/msup><\/math><\/p>","correct":false},{"option":"

51 m<\/mi>2<\/mn><\/msup>\/<\/mo>s<\/mi>2<\/mn><\/msup><\/math><\/p>","correct":false},{"option":"

52 m<\/mi>2<\/mn><\/msup>\/<\/mo>s<\/mi>2<\/mn><\/msup><\/math><\/p>","correct":false}],"solution":"

Let A = cross-section of tank
a = cross-section hole
V = velocity with which level decreases
v = velocity of effiux<\/p>

<\/figure>

From equation of continuity av = AV
\u21d2<\/mo> <\/mo>V<\/mi> <\/mo>=<\/mo> <\/mo>av<\/mi>A<\/mi><\/mfrac><\/math><\/p>

By using Bernoulli's theorem for energy per unit
volume
Energy per unit volume at point A = Energy per unit volume at point B
P<\/mi> <\/mo>+<\/mo> <\/mo>\u03c1gh<\/mi> <\/mo>+<\/mo> <\/mo>1<\/mn>2<\/mn><\/mfrac>\u03c1v<\/mi>2<\/mn><\/msup> <\/mo>=<\/mo> <\/mo>P<\/mi>+<\/mo>0<\/mn>+<\/mo>1<\/mn>2<\/mn><\/mfrac>\u03c1v<\/mi>2<\/mn><\/msup><\/math><\/p>

v<\/mi>2<\/mn><\/msup> <\/mo>=<\/mo>2<\/mn>gh<\/mi><\/mrow>1<\/mn>-<\/mo>(<\/mo>a<\/mi>A<\/mi><\/mfrac><\/mstyle>)<\/mo><\/mrow>2<\/mn><\/msup><\/mrow><\/mfrac><\/math><\/p>

= 2<\/mn>\u00d7<\/mo>10<\/mn>\u00d7<\/mo>(<\/mo>3<\/mn>-<\/mo>0<\/mn>.<\/mo>525<\/mn>)<\/mo><\/mrow>1<\/mn>-<\/mo>(<\/mo>0<\/mn>.<\/mo>1<\/mn>)<\/mo><\/mrow>2<\/mn><\/msup><\/mrow><\/mfrac> <\/mo>=<\/mo> <\/mo>50<\/mn>(<\/mo>m<\/mi>\/<\/mo>sec<\/mi>)<\/mo><\/mrow>2<\/mn><\/msup><\/math><\/p>","subject":""},"yoast_head":"\nWater is filled in a cylindrical container to a height of 3m. The ratio of the cross-sectional area of the orifice and the beaker is 0.1. The square of the speed of the liquid coming out from the orifice is (g = l0\u00a0m\/s2)\u00a0 - Infinity Learn by Sri Chaitanya<\/title>\n<meta name=\"description\" content=\"Water is filled in a cylindrical container to a height of 3m. The ratio of the cross-sectional area of the orifice and the beaker is 0.1. 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