{"id":85806,"date":"2025-06-01T03:28:31","date_gmt":"2025-06-01T03:28:31","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=85806"},"modified":"2025-06-01T03:28:31","modified_gmt":"2025-06-01T03:28:31","slug":"if-two-miscible-liquids-of-same-volume-but-different-densities-p-1-an","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/if-two-miscible-liquids-of-same-volume-but-different-densities-p-1-an\/","title":{"rendered":"If two miscible liquids of same volume but different densities P 1 an"},"content":{"rendered":"

If two miscible liquids of same volume but different densities P1<\/sub> and P2<\/sub> are mixed, then the density of the mixture is given by<\/p>\n

[amp_mcq option1=”(P1<\/sub> + P2<\/sub>) \/ 2″ option2=”2P1<\/sub>P2<\/sub> \/ (P1<\/sub> + P2<\/sub>)” option3=”2P1<\/sub>P2<\/sub> \/ (P1<\/sub> – P2<\/sub>)” option4=”P1<\/sub>P2<\/sub> \/ (P1<\/sub> + P2<\/sub>)” correct=”option1″]<\/p>\n

\n
\n
This question was previously asked in<\/div>\n
UPSC CDS-2 – 2018<\/div>\n<\/div>\n
Download PDF<\/a>Attempt Online<\/a><\/div>\n<\/div>\n
\nLet V be the volume of each liquid. The total volume of the mixture is V_total = V + V = 2V.
\nThe mass of the first liquid is m\u2081 = density \u00d7 volume = P\u2081V.
\nThe mass of the second liquid is m\u2082 = density \u00d7 volume = P\u2082V.
\nThe total mass of the mixture is m_total = m\u2081 + m\u2082 = P\u2081V + P\u2082V = (P\u2081 + P\u2082)V.
\nThe density of the mixture is \u03c1_mixture = m_total \/ V_total = (P\u2081 + P\u2082)V \/ (2V) = (P\u2081 + P\u2082) \/ 2.
\nThis formula is valid when equal volumes of two miscible liquids are mixed.
\n<\/section>\n
\n– Density is mass per unit volume.
\n– When mixing, total mass is the sum of individual masses, and total volume is the sum of individual volumes (assuming no volume change upon mixing, which is typical for miscible liquids unless otherwise specified).
\n– The calculation is based on the given condition that the liquids have the ‘same volume’.
\n<\/section>\n
\nIf two miscible liquids of *same mass* m but different densities P\u2081 and P\u2082 are mixed, the volume of the first liquid is V\u2081 = m\/P\u2081, and the volume of the second liquid is V\u2082 = m\/P\u2082. The total mass is 2m, and the total volume is V\u2081 + V\u2082 = m\/P\u2081 + m\/P\u2082 = m(P\u2081 + P\u2082)\/(P\u2081P\u2082). The density of the mixture would be (2m) \/ [m(P\u2081 + P\u2082)\/(P\u2081P\u2082)] = 2P\u2081P\u2082 \/ (P\u2081 + P\u2082), which is option B. The question specifies ‘same volume’, not ‘same mass’.
\n<\/section>\n","protected":false},"excerpt":{"rendered":"

If two miscible liquids of same volume but different densities P1 and P2 are mixed, then the density of the mixture is given by [amp_mcq option1=”(P1 + P2) \/ 2″ option2=”2P1P2 \/ (P1 + P2)” option3=”2P1P2 \/ (P1 – P2)” option4=”P1P2 \/ (P1 + P2)” correct=”option1″] This question was previously asked in UPSC CDS-2 – … <\/p>\n

Detailed SolutionIf two miscible liquids of same volume but different densities P 1 an<\/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":[1088],"tags":[1114,1160,1128],"class_list":["post-85806","post","type-post","status-publish","format-standard","hentry","category-upsc-cds-2","tag-1114","tag-physical-properties-of-materials","tag-physics","no-featured-image-padding"],"yoast_head":"\nIf two miscible liquids of same volume but different densities P 1 an<\/title>\n<meta name=\"description\" content=\"Let V be the volume of each liquid. The total volume of the mixture is V_total = V + V = 2V. The mass of the first liquid is m\u2081 = density \u00d7 volume = P\u2081V. The mass of the second liquid is m\u2082 = density \u00d7 volume = P\u2082V. The total mass of the mixture is m_total = m\u2081 + m\u2082 = P\u2081V + P\u2082V = (P\u2081 + P\u2082)V. The density of the mixture is \u03c1_mixture = m_total \/ V_total = (P\u2081 + P\u2082)V \/ (2V) = (P\u2081 + P\u2082) \/ 2. This formula is valid when equal volumes of two miscible liquids are mixed. - Density is mass per unit volume. - When mixing, total mass is the sum of individual masses, and total volume is the sum of individual volumes (assuming no volume change upon mixing, which is typical for miscible liquids unless otherwise specified). - The calculation is based on the given condition that the liquids have the 'same volume'.\" \/>\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\/if-two-miscible-liquids-of-same-volume-but-different-densities-p-1-an\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"If two miscible liquids of same volume but different densities P 1 an\" \/>\n<meta property=\"og:description\" content=\"Let V be the volume of each liquid. The total volume of the mixture is V_total = V + V = 2V. The mass of the first liquid is m\u2081 = density \u00d7 volume = P\u2081V. The mass of the second liquid is m\u2082 = density \u00d7 volume = P\u2082V. The total mass of the mixture is m_total = m\u2081 + m\u2082 = P\u2081V + P\u2082V = (P\u2081 + P\u2082)V. The density of the mixture is \u03c1_mixture = m_total \/ V_total = (P\u2081 + P\u2082)V \/ (2V) = (P\u2081 + P\u2082) \/ 2. This formula is valid when equal volumes of two miscible liquids are mixed. - Density is mass per unit volume. - When mixing, total mass is the sum of individual masses, and total volume is the sum of individual volumes (assuming no volume change upon mixing, which is typical for miscible liquids unless otherwise specified). - The calculation is based on the given condition that the liquids have the 'same volume'.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/exam.pscnotes.com\/mcq\/if-two-miscible-liquids-of-same-volume-but-different-densities-p-1-an\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ and Quiz for Exams\" \/>\n<meta property=\"article:published_time\" content=\"2025-06-01T03:28:31+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":"If two miscible liquids of same volume but different densities P 1 an","description":"Let V be the volume of each liquid. The total volume of the mixture is V_total = V + V = 2V. The mass of the first liquid is m\u2081 = density \u00d7 volume = P\u2081V. The mass of the second liquid is m\u2082 = density \u00d7 volume = P\u2082V. The total mass of the mixture is m_total = m\u2081 + m\u2082 = P\u2081V + P\u2082V = (P\u2081 + P\u2082)V. The density of the mixture is \u03c1_mixture = m_total \/ V_total = (P\u2081 + P\u2082)V \/ (2V) = (P\u2081 + P\u2082) \/ 2. This formula is valid when equal volumes of two miscible liquids are mixed. - Density is mass per unit volume. - When mixing, total mass is the sum of individual masses, and total volume is the sum of individual volumes (assuming no volume change upon mixing, which is typical for miscible liquids unless otherwise specified). - The calculation is based on the given condition that the liquids have the 'same volume'.","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\/if-two-miscible-liquids-of-same-volume-but-different-densities-p-1-an\/","og_locale":"en_US","og_type":"article","og_title":"If two miscible liquids of same volume but different densities P 1 an","og_description":"Let V be the volume of each liquid. The total volume of the mixture is V_total = V + V = 2V. The mass of the first liquid is m\u2081 = density \u00d7 volume = P\u2081V. The mass of the second liquid is m\u2082 = density \u00d7 volume = P\u2082V. The total mass of the mixture is m_total = m\u2081 + m\u2082 = P\u2081V + P\u2082V = (P\u2081 + P\u2082)V. The density of the mixture is \u03c1_mixture = m_total \/ V_total = (P\u2081 + P\u2082)V \/ (2V) = (P\u2081 + P\u2082) \/ 2. This formula is valid when equal volumes of two miscible liquids are mixed. - Density is mass per unit volume. - When mixing, total mass is the sum of individual masses, and total volume is the sum of individual volumes (assuming no volume change upon mixing, which is typical for miscible liquids unless otherwise specified). - The calculation is based on the given condition that the liquids have the 'same volume'.","og_url":"https:\/\/exam.pscnotes.com\/mcq\/if-two-miscible-liquids-of-same-volume-but-different-densities-p-1-an\/","og_site_name":"MCQ and Quiz for Exams","article_published_time":"2025-06-01T03:28:31+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\/if-two-miscible-liquids-of-same-volume-but-different-densities-p-1-an\/","url":"https:\/\/exam.pscnotes.com\/mcq\/if-two-miscible-liquids-of-same-volume-but-different-densities-p-1-an\/","name":"If two miscible liquids of same volume but different densities P 1 an","isPartOf":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#website"},"datePublished":"2025-06-01T03:28:31+00:00","dateModified":"2025-06-01T03:28:31+00:00","author":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209"},"description":"Let V be the volume of each liquid. The total volume of the mixture is V_total = V + V = 2V. The mass of the first liquid is m\u2081 = density \u00d7 volume = P\u2081V. The mass of the second liquid is m\u2082 = density \u00d7 volume = P\u2082V. The total mass of the mixture is m_total = m\u2081 + m\u2082 = P\u2081V + P\u2082V = (P\u2081 + P\u2082)V. The density of the mixture is \u03c1_mixture = m_total \/ V_total = (P\u2081 + P\u2082)V \/ (2V) = (P\u2081 + P\u2082) \/ 2. This formula is valid when equal volumes of two miscible liquids are mixed. - Density is mass per unit volume. - When mixing, total mass is the sum of individual masses, and total volume is the sum of individual volumes (assuming no volume change upon mixing, which is typical for miscible liquids unless otherwise specified). - The calculation is based on the given condition that the liquids have the 'same volume'.","breadcrumb":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/if-two-miscible-liquids-of-same-volume-but-different-densities-p-1-an\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/exam.pscnotes.com\/mcq\/if-two-miscible-liquids-of-same-volume-but-different-densities-p-1-an\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/exam.pscnotes.com\/mcq\/if-two-miscible-liquids-of-same-volume-but-different-densities-p-1-an\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/exam.pscnotes.com\/mcq\/"},{"@type":"ListItem","position":2,"name":"UPSC CDS-2","item":"https:\/\/exam.pscnotes.com\/mcq\/category\/upsc-cds-2\/"},{"@type":"ListItem","position":3,"name":"If two miscible liquids of same volume but different densities P 1 an"}]},{"@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\/85806","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=85806"}],"version-history":[{"count":0,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts\/85806\/revisions"}],"wp:attachment":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/media?parent=85806"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/categories?post=85806"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/tags?post=85806"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}