{"id":88840,"date":"2025-06-01T07:23:16","date_gmt":"2025-06-01T07:23:16","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=88840"},"modified":"2025-06-01T07:23:16","modified_gmt":"2025-06-01T07:23:16","slug":"an-object-is-made-of-two-equal-parts-by-volume-one-part-has-density","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/an-object-is-made-of-two-equal-parts-by-volume-one-part-has-density\/","title":{"rendered":"An object is made of two equal parts by volume; one part has density $"},"content":{"rendered":"

An object is made of two equal parts by volume; one part has density $\\rho_0$ and the other part has density $2\\rho_0$. What is the average density of the object?<\/p>\n

[amp_mcq option1=”$3\\rho_0$” option2=”$\\frac{3}{2}\\rho_0$” option3=”$\\rho_0$” option4=”$\\frac{1}{2}\\rho_0$” correct=”option2″]<\/p>\n

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This question was previously asked in<\/div>\n
UPSC NDA-2 – 2022<\/div>\n<\/div>\n
Download PDF<\/a>Attempt Online<\/a><\/div>\n<\/div>\n
\nLet V be the total volume of the object. The object is made of two equal parts by volume, so the volume of each part is $V_1 = V_2 = V\/2$.
\nLet $\\rho_1$ be the density of the first part and $\\rho_2$ be the density of the second part.
\nGiven: $\\rho_1 = \\rho_0$ and $\\rho_2 = 2\\rho_0$.
\nThe mass of the first part is $m_1 = \\rho_1 \\times V_1 = \\rho_0 \\times (V\/2)$.
\nThe mass of the second part is $m_2 = \\rho_2 \\times V_2 = 2\\rho_0 \\times (V\/2) = \\rho_0 V$.
\nThe total mass of the object is $M = m_1 + m_2 = \\rho_0 (V\/2) + \\rho_0 V = \\rho_0 V (\\frac{1}{2} + 1) = \\rho_0 V (\\frac{3}{2})$.
\nThe total volume of the object is $V_{\\text{total}} = V_1 + V_2 = V\/2 + V\/2 = V$.
\nThe average density of the object is $\\rho_{\\text{avg}} = \\frac{M}{V_{\\text{total}}} = \\frac{\\rho_0 V (3\/2)}{V} = \\frac{3}{2}\\rho_0$.
\n<\/section>\n
\nWhen calculating average density for parts of equal volume, the average density is the simple arithmetic mean of the densities. However, in this case, the masses are different. The calculation involves finding the total mass and dividing by the total volume.
\n<\/section>\n
\nIf the parts were of equal mass instead of equal volume, the calculation would be different, involving the reciprocal of the average of reciprocals (harmonic mean of densities).
\n<\/section>\n","protected":false},"excerpt":{"rendered":"

An object is made of two equal parts by volume; one part has density $\\rho_0$ and the other part has density $2\\rho_0$. What is the average density of the object? [amp_mcq option1=”$3\\rho_0$” option2=”$\\frac{3}{2}\\rho_0$” option3=”$\\rho_0$” option4=”$\\frac{1}{2}\\rho_0$” correct=”option2″] This question was previously asked in UPSC NDA-2 – 2022 Download PDFAttempt Online Let V be the total volume … <\/p>\n

Detailed SolutionAn object is made of two equal parts by volume; one part has density $<\/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":[1094],"tags":[1108,1160,1128],"class_list":["post-88840","post","type-post","status-publish","format-standard","hentry","category-upsc-nda-2","tag-1108","tag-physical-properties-of-materials","tag-physics","no-featured-image-padding"],"yoast_head":"\nAn object is made of two equal parts by volume; one part has density $<\/title>\n<meta name=\"description\" content=\"Let V be the total volume of the object. The object is made of two equal parts by volume, so the volume of each part is $V_1 = V_2 = V\/2$. Let $rho_1$ be the density of the first part and $rho_2$ be the density of the second part. Given: $rho_1 = rho_0$ and $rho_2 = 2rho_0$. The mass of the first part is $m_1 = rho_1 times V_1 = rho_0 times (V\/2)$. The mass of the second part is $m_2 = rho_2 times V_2 = 2rho_0 times (V\/2) = rho_0 V$. The total mass of the object is $M = m_1 + m_2 = rho_0 (V\/2) + rho_0 V = rho_0 V (frac{1}{2} + 1) = rho_0 V (frac{3}{2})$. The total volume of the object is $V_{text{total}} = V_1 + V_2 = V\/2 + V\/2 = V$. The average density of the object is $rho_{text{avg}} = frac{M}{V_{text{total}}} = frac{rho_0 V (3\/2)}{V} = frac{3}{2}rho_0$. When calculating average density for parts of equal volume, the average density is the simple arithmetic mean of the densities. However, in this case, the masses are different. The calculation involves finding the total mass and dividing by the total 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\/an-object-is-made-of-two-equal-parts-by-volume-one-part-has-density\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"An object is made of two equal parts by volume; one part has density $\" \/>\n<meta property=\"og:description\" content=\"Let V be the total volume of the object. The object is made of two equal parts by volume, so the volume of each part is $V_1 = V_2 = V\/2$. Let $rho_1$ be the density of the first part and $rho_2$ be the density of the second part. Given: $rho_1 = rho_0$ and $rho_2 = 2rho_0$. The mass of the first part is $m_1 = rho_1 times V_1 = rho_0 times (V\/2)$. The mass of the second part is $m_2 = rho_2 times V_2 = 2rho_0 times (V\/2) = rho_0 V$. The total mass of the object is $M = m_1 + m_2 = rho_0 (V\/2) + rho_0 V = rho_0 V (frac{1}{2} + 1) = rho_0 V (frac{3}{2})$. The total volume of the object is $V_{text{total}} = V_1 + V_2 = V\/2 + V\/2 = V$. The average density of the object is $rho_{text{avg}} = frac{M}{V_{text{total}}} = frac{rho_0 V (3\/2)}{V} = frac{3}{2}rho_0$. When calculating average density for parts of equal volume, the average density is the simple arithmetic mean of the densities. However, in this case, the masses are different. The calculation involves finding the total mass and dividing by the total volume.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/exam.pscnotes.com\/mcq\/an-object-is-made-of-two-equal-parts-by-volume-one-part-has-density\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ and Quiz for Exams\" \/>\n<meta property=\"article:published_time\" content=\"2025-06-01T07:23:16+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":"An object is made of two equal parts by volume; one part has density $","description":"Let V be the total volume of the object. The object is made of two equal parts by volume, so the volume of each part is $V_1 = V_2 = V\/2$. Let $rho_1$ be the density of the first part and $rho_2$ be the density of the second part. Given: $rho_1 = rho_0$ and $rho_2 = 2rho_0$. The mass of the first part is $m_1 = rho_1 times V_1 = rho_0 times (V\/2)$. The mass of the second part is $m_2 = rho_2 times V_2 = 2rho_0 times (V\/2) = rho_0 V$. The total mass of the object is $M = m_1 + m_2 = rho_0 (V\/2) + rho_0 V = rho_0 V (frac{1}{2} + 1) = rho_0 V (frac{3}{2})$. The total volume of the object is $V_{text{total}} = V_1 + V_2 = V\/2 + V\/2 = V$. The average density of the object is $rho_{text{avg}} = frac{M}{V_{text{total}}} = frac{rho_0 V (3\/2)}{V} = frac{3}{2}rho_0$. When calculating average density for parts of equal volume, the average density is the simple arithmetic mean of the densities. However, in this case, the masses are different. The calculation involves finding the total mass and dividing by the total 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\/an-object-is-made-of-two-equal-parts-by-volume-one-part-has-density\/","og_locale":"en_US","og_type":"article","og_title":"An object is made of two equal parts by volume; one part has density $","og_description":"Let V be the total volume of the object. The object is made of two equal parts by volume, so the volume of each part is $V_1 = V_2 = V\/2$. Let $rho_1$ be the density of the first part and $rho_2$ be the density of the second part. Given: $rho_1 = rho_0$ and $rho_2 = 2rho_0$. The mass of the first part is $m_1 = rho_1 times V_1 = rho_0 times (V\/2)$. The mass of the second part is $m_2 = rho_2 times V_2 = 2rho_0 times (V\/2) = rho_0 V$. The total mass of the object is $M = m_1 + m_2 = rho_0 (V\/2) + rho_0 V = rho_0 V (frac{1}{2} + 1) = rho_0 V (frac{3}{2})$. The total volume of the object is $V_{text{total}} = V_1 + V_2 = V\/2 + V\/2 = V$. The average density of the object is $rho_{text{avg}} = frac{M}{V_{text{total}}} = frac{rho_0 V (3\/2)}{V} = frac{3}{2}rho_0$. When calculating average density for parts of equal volume, the average density is the simple arithmetic mean of the densities. However, in this case, the masses are different. The calculation involves finding the total mass and dividing by the total volume.","og_url":"https:\/\/exam.pscnotes.com\/mcq\/an-object-is-made-of-two-equal-parts-by-volume-one-part-has-density\/","og_site_name":"MCQ and Quiz for Exams","article_published_time":"2025-06-01T07:23:16+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-object-is-made-of-two-equal-parts-by-volume-one-part-has-density\/","url":"https:\/\/exam.pscnotes.com\/mcq\/an-object-is-made-of-two-equal-parts-by-volume-one-part-has-density\/","name":"An object is made of two equal parts by volume; one part has density $","isPartOf":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#website"},"datePublished":"2025-06-01T07:23:16+00:00","dateModified":"2025-06-01T07:23:16+00:00","author":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209"},"description":"Let V be the total volume of the object. The object is made of two equal parts by volume, so the volume of each part is $V_1 = V_2 = V\/2$. Let $\\rho_1$ be the density of the first part and $\\rho_2$ be the density of the second part. Given: $\\rho_1 = \\rho_0$ and $\\rho_2 = 2\\rho_0$. The mass of the first part is $m_1 = \\rho_1 \\times V_1 = \\rho_0 \\times (V\/2)$. The mass of the second part is $m_2 = \\rho_2 \\times V_2 = 2\\rho_0 \\times (V\/2) = \\rho_0 V$. The total mass of the object is $M = m_1 + m_2 = \\rho_0 (V\/2) + \\rho_0 V = \\rho_0 V (\\frac{1}{2} + 1) = \\rho_0 V (\\frac{3}{2})$. The total volume of the object is $V_{\\text{total}} = V_1 + V_2 = V\/2 + V\/2 = V$. The average density of the object is $\\rho_{\\text{avg}} = \\frac{M}{V_{\\text{total}}} = \\frac{\\rho_0 V (3\/2)}{V} = \\frac{3}{2}\\rho_0$. When calculating average density for parts of equal volume, the average density is the simple arithmetic mean of the densities. However, in this case, the masses are different. The calculation involves finding the total mass and dividing by the total volume.","breadcrumb":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/an-object-is-made-of-two-equal-parts-by-volume-one-part-has-density\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/exam.pscnotes.com\/mcq\/an-object-is-made-of-two-equal-parts-by-volume-one-part-has-density\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/exam.pscnotes.com\/mcq\/an-object-is-made-of-two-equal-parts-by-volume-one-part-has-density\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/exam.pscnotes.com\/mcq\/"},{"@type":"ListItem","position":2,"name":"UPSC NDA-2","item":"https:\/\/exam.pscnotes.com\/mcq\/category\/upsc-nda-2\/"},{"@type":"ListItem","position":3,"name":"An object is made of two equal parts by volume; one part has density $"}]},{"@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\/88840","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=88840"}],"version-history":[{"count":0,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts\/88840\/revisions"}],"wp:attachment":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/media?parent=88840"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/categories?post=88840"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/tags?post=88840"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}