{"id":87343,"date":"2025-06-01T06:41:18","date_gmt":"2025-06-01T06:41:18","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=87343"},"modified":"2025-06-01T06:41:18","modified_gmt":"2025-06-01T06:41:18","slug":"a-container-is-first-filled-with-water-and-then-the-entire-water-is-re","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/a-container-is-first-filled-with-water-and-then-the-entire-water-is-re\/","title":{"rendered":"A container is first filled with water and then the entire water is re"},"content":{"rendered":"

A container is first filled with water and then the entire water is replaced by mercury. Mercury has a density of 13\u00b76 \u00d7 10\u00b3 kg\/m\u00b3. If X is the weight of the water and Y is the weight of the mercury, then<\/p>\n

[amp_mcq option1=”X = Y” option2=”X = 13\u00b76 Y” option3=”Y = 13\u00b76 X” option4=”None of the above” correct=”option3″]<\/p>\n

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\n
This question was previously asked in<\/div>\n
UPSC NDA-1 – 2016<\/div>\n<\/div>\n
Download PDF<\/a>Attempt Online<\/a><\/div>\n<\/div>\n
The weight of an object is given by W = m * g, where m is the mass and g is the acceleration due to gravity. The mass of a substance filling a container of volume V is given by m = \u03c1 * V, where \u03c1 is the density of the substance.
\nFor water, the weight X is given by X = \u03c1water<\/sub> * V * g.
\nFor mercury, the weight Y is given by Y = \u03c1mercury<\/sub> * V * g.
\nThe density of water is approximately 1.0 \u00d7 10\u00b3 kg\/m\u00b3.
\nThe density of mercury is given as 13.6 \u00d7 10\u00b3 kg\/m\u00b3.
\nTaking the ratio of the weights:
\nY \/ X = (\u03c1mercury<\/sub> * V * g) \/ (\u03c1water<\/sub> * V * g)
\nY \/ X = \u03c1mercury<\/sub> \/ \u03c1water<\/sub>
\nY \/ X = (13.6 \u00d7 10\u00b3) \/ (1.0 \u00d7 10\u00b3) = 13.6
\nTherefore, Y = 13.6 X.
\n<\/section>\n
Weight depends on mass and gravitational acceleration. Mass is proportional to density for a fixed volume. The ratio of weights for the same volume of different substances is equal to the ratio of their densities.<\/section>\n
The density of water varies slightly with temperature and pressure, but 1000 kg\/m\u00b3 is a standard value at 4\u00b0C. The acceleration due to gravity (g) is the same for both substances in the same location, so it cancels out in the ratio.<\/section>\n","protected":false},"excerpt":{"rendered":"

A container is first filled with water and then the entire water is replaced by mercury. Mercury has a density of 13\u00b76 \u00d7 10\u00b3 kg\/m\u00b3. If X is the weight of the water and Y is the weight of the mercury, then [amp_mcq option1=”X = Y” option2=”X = 13\u00b76 Y” option3=”Y = 13\u00b76 X” option4=”None … <\/p>\n

Detailed SolutionA container is first filled with water and then the entire water is re<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1093],"tags":[1098,1129,1128],"class_list":["post-87343","post","type-post","status-publish","format-standard","hentry","category-upsc-nda-1","tag-1098","tag-mechanics","tag-physics","no-featured-image-padding"],"yoast_head":"\nA container is first filled with water and then the entire water is re<\/title>\n<meta name=\"description\" content=\"The weight of an object is given by W = m * g, where m is the mass and g is the acceleration due to gravity. The mass of a substance filling a container of volume V is given by m = \u03c1 * V, where \u03c1 is the density of the substance. For water, the weight X is given by X = \u03c1water * V * g. For mercury, the weight Y is given by Y = \u03c1mercury * V * g. The density of water is approximately 1.0 \u00d7 10\u00b3 kg\/m\u00b3. The density of mercury is given as 13.6 \u00d7 10\u00b3 kg\/m\u00b3. Taking the ratio of the weights: Y \/ X = (\u03c1mercury * V * g) \/ (\u03c1water * V * g) Y \/ X = \u03c1mercury \/ \u03c1water Y \/ X = (13.6 \u00d7 10\u00b3) \/ (1.0 \u00d7 10\u00b3) = 13.6 Therefore, Y = 13.6 X. Weight depends on mass and gravitational acceleration. Mass is proportional to density for a fixed volume. The ratio of weights for the same volume of different substances is equal to the ratio of their densities.\" \/>\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\/a-container-is-first-filled-with-water-and-then-the-entire-water-is-re\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"A container is first filled with water and then the entire water is re\" \/>\n<meta property=\"og:description\" content=\"The weight of an object is given by W = m * g, where m is the mass and g is the acceleration due to gravity. The mass of a substance filling a container of volume V is given by m = \u03c1 * V, where \u03c1 is the density of the substance. For water, the weight X is given by X = \u03c1water * V * g. For mercury, the weight Y is given by Y = \u03c1mercury * V * g. The density of water is approximately 1.0 \u00d7 10\u00b3 kg\/m\u00b3. The density of mercury is given as 13.6 \u00d7 10\u00b3 kg\/m\u00b3. Taking the ratio of the weights: Y \/ X = (\u03c1mercury * V * g) \/ (\u03c1water * V * g) Y \/ X = \u03c1mercury \/ \u03c1water Y \/ X = (13.6 \u00d7 10\u00b3) \/ (1.0 \u00d7 10\u00b3) = 13.6 Therefore, Y = 13.6 X. Weight depends on mass and gravitational acceleration. Mass is proportional to density for a fixed volume. The ratio of weights for the same volume of different substances is equal to the ratio of their densities.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/exam.pscnotes.com\/mcq\/a-container-is-first-filled-with-water-and-then-the-entire-water-is-re\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ and Quiz for Exams\" \/>\n<meta property=\"article:published_time\" content=\"2025-06-01T06:41:18+00:00\" \/>\n<meta name=\"author\" content=\"rawan239\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"rawan239\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 minute\" \/>\n<!-- \/ Yoast SEO Premium plugin. -->","yoast_head_json":{"title":"A container is first filled with water and then the entire water is re","description":"The weight of an object is given by W = m * g, where m is the mass and g is the acceleration due to gravity. The mass of a substance filling a container of volume V is given by m = \u03c1 * V, where \u03c1 is the density of the substance. For water, the weight X is given by X = \u03c1water * V * g. For mercury, the weight Y is given by Y = \u03c1mercury * V * g. The density of water is approximately 1.0 \u00d7 10\u00b3 kg\/m\u00b3. The density of mercury is given as 13.6 \u00d7 10\u00b3 kg\/m\u00b3. Taking the ratio of the weights: Y \/ X = (\u03c1mercury * V * g) \/ (\u03c1water * V * g) Y \/ X = \u03c1mercury \/ \u03c1water Y \/ X = (13.6 \u00d7 10\u00b3) \/ (1.0 \u00d7 10\u00b3) = 13.6 Therefore, Y = 13.6 X. Weight depends on mass and gravitational acceleration. Mass is proportional to density for a fixed volume. The ratio of weights for the same volume of different substances is equal to the ratio of their densities.","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\/a-container-is-first-filled-with-water-and-then-the-entire-water-is-re\/","og_locale":"en_US","og_type":"article","og_title":"A container is first filled with water and then the entire water is re","og_description":"The weight of an object is given by W = m * g, where m is the mass and g is the acceleration due to gravity. The mass of a substance filling a container of volume V is given by m = \u03c1 * V, where \u03c1 is the density of the substance. For water, the weight X is given by X = \u03c1water * V * g. For mercury, the weight Y is given by Y = \u03c1mercury * V * g. The density of water is approximately 1.0 \u00d7 10\u00b3 kg\/m\u00b3. The density of mercury is given as 13.6 \u00d7 10\u00b3 kg\/m\u00b3. Taking the ratio of the weights: Y \/ X = (\u03c1mercury * V * g) \/ (\u03c1water * V * g) Y \/ X = \u03c1mercury \/ \u03c1water Y \/ X = (13.6 \u00d7 10\u00b3) \/ (1.0 \u00d7 10\u00b3) = 13.6 Therefore, Y = 13.6 X. Weight depends on mass and gravitational acceleration. Mass is proportional to density for a fixed volume. The ratio of weights for the same volume of different substances is equal to the ratio of their densities.","og_url":"https:\/\/exam.pscnotes.com\/mcq\/a-container-is-first-filled-with-water-and-then-the-entire-water-is-re\/","og_site_name":"MCQ and Quiz for Exams","article_published_time":"2025-06-01T06:41:18+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\/a-container-is-first-filled-with-water-and-then-the-entire-water-is-re\/","url":"https:\/\/exam.pscnotes.com\/mcq\/a-container-is-first-filled-with-water-and-then-the-entire-water-is-re\/","name":"A container is first filled with water and then the entire water is re","isPartOf":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#website"},"datePublished":"2025-06-01T06:41:18+00:00","dateModified":"2025-06-01T06:41:18+00:00","author":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209"},"description":"The weight of an object is given by W = m * g, where m is the mass and g is the acceleration due to gravity. The mass of a substance filling a container of volume V is given by m = \u03c1 * V, where \u03c1 is the density of the substance. For water, the weight X is given by X = \u03c1water * V * g. For mercury, the weight Y is given by Y = \u03c1mercury * V * g. The density of water is approximately 1.0 \u00d7 10\u00b3 kg\/m\u00b3. The density of mercury is given as 13.6 \u00d7 10\u00b3 kg\/m\u00b3. Taking the ratio of the weights: Y \/ X = (\u03c1mercury * V * g) \/ (\u03c1water * V * g) Y \/ X = \u03c1mercury \/ \u03c1water Y \/ X = (13.6 \u00d7 10\u00b3) \/ (1.0 \u00d7 10\u00b3) = 13.6 Therefore, Y = 13.6 X. Weight depends on mass and gravitational acceleration. Mass is proportional to density for a fixed volume. The ratio of weights for the same volume of different substances is equal to the ratio of their densities.","breadcrumb":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/a-container-is-first-filled-with-water-and-then-the-entire-water-is-re\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/exam.pscnotes.com\/mcq\/a-container-is-first-filled-with-water-and-then-the-entire-water-is-re\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/exam.pscnotes.com\/mcq\/a-container-is-first-filled-with-water-and-then-the-entire-water-is-re\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/exam.pscnotes.com\/mcq\/"},{"@type":"ListItem","position":2,"name":"UPSC NDA-1","item":"https:\/\/exam.pscnotes.com\/mcq\/category\/upsc-nda-1\/"},{"@type":"ListItem","position":3,"name":"A container is first filled with water and then the entire water is re"}]},{"@type":"WebSite","@id":"https:\/\/exam.pscnotes.com\/mcq\/#website","url":"https:\/\/exam.pscnotes.com\/mcq\/","name":"MCQ and Quiz for Exams","description":"","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/exam.pscnotes.com\/mcq\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"en-US"},{"@type":"Person","@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209","name":"rawan239","image":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/image\/","url":"https:\/\/secure.gravatar.com\/avatar\/761a7274f9cce048fa5b921221e7934820d74514df93ef195a9d22af0c1c9001?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/761a7274f9cce048fa5b921221e7934820d74514df93ef195a9d22af0c1c9001?s=96&d=mm&r=g","caption":"rawan239"},"sameAs":["https:\/\/exam.pscnotes.com"],"url":"https:\/\/exam.pscnotes.com\/mcq\/author\/rawan239\/"}]}},"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts\/87343","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/comments?post=87343"}],"version-history":[{"count":0,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts\/87343\/revisions"}],"wp:attachment":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/media?parent=87343"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/categories?post=87343"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/tags?post=87343"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}