{"id":7173,"date":"2024-04-15T02:40:43","date_gmt":"2024-04-15T02:40:43","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=7173"},"modified":"2024-04-15T02:40:43","modified_gmt":"2024-04-15T02:40:43","slug":"an-open-cubical-tank-of-2-m-side-is-filled-with-water-if-the-tank-is-rotated-with-an-acceleration-such-that-half-of-the-water-spills-out-then-the-acceleration-is-equal-to-a-fractextg3","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/an-open-cubical-tank-of-2-m-side-is-filled-with-water-if-the-tank-is-rotated-with-an-acceleration-such-that-half-of-the-water-spills-out-then-the-acceleration-is-equal-to-a-fractextg3\/","title":{"rendered":"An open cubical tank of 2 m side is filled with water. If the tank is rotated with an acceleration such that half of the water spills out, then the acceleration is equal to A. $$\\frac{{\\text{g}}}{3}$$ B. $$\\frac{{\\text{g}}}{2}$$ C. $$\\frac{{2{\\text{g}}}}{3}$$ D. $${\\text{g}}$$"},"content":{"rendered":"<p>[amp_mcq option1=&#8221;$$\\frac{{\\text{g}}}{3}$$&#8221; option2=&#8221;$$\\frac{{\\text{g}}}{2}$$&#8221; option3=&#8221;$$\\frac{{2{\\text{g}}}}{3}$$&#8221; option4=&#8221;$${\\text{g}}$$&#8221; correct=&#8221;option1&#8243;]<!--more--><\/p>\n<p>The correct answer is $\\boxed{\\frac{{\\text{g}}}{3}}$.<\/p>\n<p>The centripetal acceleration of the water at the edge of the tank is $\\frac{v^2}{r}$, where $v$ is the tangential velocity of the water and $r$ is the radius of the tank. The tangential velocity of the water is equal to the product of the angular velocity of the tank, $\\omega$, and the radius of the tank. The angular velocity of the tank is equal to the acceleration of the tank, $a$, divided by the radius of the tank. Therefore, the centripetal acceleration of the water is equal to $\\frac{a^2r}{r^2} = a$.<\/p>\n<p>The water will spill out of the tank when the centripetal acceleration of the water is greater than the acceleration due to gravity, $g$. Therefore, the acceleration of the tank must be greater than or equal to $\\frac{g}{r}$.<\/p>\n<p>The radius of the tank is $2\\text{ m}$, so the acceleration of the tank must be greater than or equal to $\\frac{g}{2\\text{ m}} = \\frac{{\\text{g}}}{2}$.<\/p>\n<p>The options are:<\/p>\n<ul>\n<li>$\\boxed{\\frac{{\\text{g}}}{3}}$: This is the acceleration of the tank when half of the water spills out.<\/li>\n<li>$\\frac{{\\text{g}}}{2}$: This is the acceleration of the tank when all of the water spills out.<\/li>\n<li>$\\frac{{2{\\text{g}}}}{3}$: This is the acceleration of the tank when the water at the edge of the tank is at the point of spilling out.<\/li>\n<li>${\\text{g}}$: This is the acceleration due to gravity.<\/li>\n<\/ul>\n<p>Therefore, the correct answer is $\\boxed{\\frac{{\\text{g}}}{3}}$.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>[amp_mcq option1=&#8221;$$\\frac{{\\text{g}}}{3}$$&#8221; option2=&#8221;$$\\frac{{\\text{g}}}{2}$$&#8221; option3=&#8221;$$\\frac{{2{\\text{g}}}}{3}$$&#8221; option4=&#8221;$${\\text{g}}$$&#8221; correct=&#8221;option1&#8243;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[648],"tags":[],"class_list":["post-7173","post","type-post","status-publish","format-standard","hentry","category-hydraulics-and-fluid-mechanics","no-featured-image-padding"],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v22.2 (Yoast SEO v23.3) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>An open cubical tank of 2 m side is filled with water. If the tank is rotated with an acceleration such that half of the water spills out, then the acceleration is equal to A. $$\\frac{{\\text{g}}}{3}$$ B. $$\\frac{{\\text{g}}}{2}$$ C. $$\\frac{{2{\\text{g}}}}{3}$$ D. $${\\text{g}}$$<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/exam.pscnotes.com\/mcq\/an-open-cubical-tank-of-2-m-side-is-filled-with-water-if-the-tank-is-rotated-with-an-acceleration-such-that-half-of-the-water-spills-out-then-the-acceleration-is-equal-to-a-fractextg3\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"An open cubical tank of 2 m side is filled with water. 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If the tank is rotated with an acceleration such that half of the water spills out, then the acceleration is equal to A. $$\\frac{{\\text{g}}}{3}$$ B. $$\\frac{{\\text{g}}}{2}$$ C. $$\\frac{{2{\\text{g}}}}{3}$$ D. $${\\text{g}}$$","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/exam.pscnotes.com\/mcq\/an-open-cubical-tank-of-2-m-side-is-filled-with-water-if-the-tank-is-rotated-with-an-acceleration-such-that-half-of-the-water-spills-out-then-the-acceleration-is-equal-to-a-fractextg3\/","og_locale":"en_US","og_type":"article","og_title":"An open cubical tank of 2 m side is filled with water. If the tank is rotated with an acceleration such that half of the water spills out, then the acceleration is equal to A. $$\\frac{{\\text{g}}}{3}$$ B. $$\\frac{{\\text{g}}}{2}$$ C. $$\\frac{{2{\\text{g}}}}{3}$$ D. $${\\text{g}}$$","og_description":"[amp_mcq option1=&#8221;$$frac{{text{g}}}{3}$$&#8221; option2=&#8221;$$frac{{text{g}}}{2}$$&#8221; option3=&#8221;$$frac{{2{text{g}}}}{3}$$&#8221; option4=&#8221;$${text{g}}$$&#8221; correct=&#8221;option1&#8243;]","og_url":"https:\/\/exam.pscnotes.com\/mcq\/an-open-cubical-tank-of-2-m-side-is-filled-with-water-if-the-tank-is-rotated-with-an-acceleration-such-that-half-of-the-water-spills-out-then-the-acceleration-is-equal-to-a-fractextg3\/","og_site_name":"MCQ and Quiz for Exams","article_published_time":"2024-04-15T02:40:43+00:00","author":"rawan239","twitter_card":"summary_large_image","twitter_misc":{"Written by":"rawan239","Est. reading time":"1 minute"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/exam.pscnotes.com\/mcq\/an-open-cubical-tank-of-2-m-side-is-filled-with-water-if-the-tank-is-rotated-with-an-acceleration-such-that-half-of-the-water-spills-out-then-the-acceleration-is-equal-to-a-fractextg3\/","url":"https:\/\/exam.pscnotes.com\/mcq\/an-open-cubical-tank-of-2-m-side-is-filled-with-water-if-the-tank-is-rotated-with-an-acceleration-such-that-half-of-the-water-spills-out-then-the-acceleration-is-equal-to-a-fractextg3\/","name":"An open cubical tank of 2 m side is filled with water. 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