{"id":87689,"date":"2025-06-01T06:51:18","date_gmt":"2025-06-01T06:51:18","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=87689"},"modified":"2025-06-01T06:51:18","modified_gmt":"2025-06-01T06:51:18","slug":"suppose-there-are-two-planets-1-and-2-having-the-same-density-but-th","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/suppose-there-are-two-planets-1-and-2-having-the-same-density-but-th\/","title":{"rendered":"Suppose there are two planets, 1 and 2, having the same density but th"},"content":{"rendered":"

Suppose there are two planets, 1 and 2, having the same density but their radii are R\u2081 and R\u2082 respectively, where R\u2081 > R\u2082. The accelerations due to gravity on the surface of these planets are related as<\/p>\n

[amp_mcq option1=”g\u2081 > g\u2082” option2=”g\u2081 < g\u2082\" option3=\"g\u2081 = g\u2082\" option4=\"Can't say anything\" correct=\"option1\"]\n\n\n\n

\n
\n
This question was previously asked in<\/div>\n
UPSC NDA-1 – 2019<\/div>\n<\/div>\n
Download PDF<\/a>Attempt Online<\/a><\/div>\n<\/div>\n
\nIf two planets have the same density but different radii R\u2081 and R\u2082 with R\u2081 > R\u2082, the acceleration due to gravity on the surface of the planet with the larger radius (Planet 1) will be greater than that on the surface of the planet with the smaller radius (Planet 2), i.e., g\u2081 > g\u2082.
\n<\/section>\n
\n– The acceleration due to gravity on the surface of a sphere is given by g = GM\/R\u00b2, where G is the gravitational constant, M is the mass, and R is the radius.
\n– The mass M can be expressed as M = \u03c1 * V, where \u03c1 is the density and V is the volume. For a sphere, V = (4\/3)\u03c0R\u00b3.
\n– Substituting this into the gravity formula: g = G * (\u03c1 * (4\/3)\u03c0R\u00b3) \/ R\u00b2 = (4\/3)\u03c0G\u03c1R.
\n– Since the density \u03c1 and constants G, 4\/3, and \u03c0 are the same for both planets, the acceleration due to gravity is directly proportional to the radius (g \u221d R).
\n– Given R\u2081 > R\u2082, it follows that g\u2081 > g\u2082.
\n<\/section>\n
\nThis relationship shows that for objects of the same density, larger objects exert stronger gravitational pull at their surface compared to smaller objects. This is because the increase in mass (proportional to R\u00b3) outpaces the increase in distance from the center (proportional to R\u00b2).
\n<\/section>\n","protected":false},"excerpt":{"rendered":"

Suppose there are two planets, 1 and 2, having the same density but their radii are R\u2081 and R\u2082 respectively, where R\u2081 > R\u2082. The accelerations due to gravity on the surface of these planets are related as [amp_mcq option1=”g\u2081 > g\u2082” option2=”g\u2081 < g\u2082\" option3=\"g\u2081 = g\u2082\" option4=\"Can't say anything\" correct=\"option1\"] This question was ... \n\n

Detailed SolutionSuppose there are two planets, 1 and 2, having the same density but th<\/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":[1119,1129,1128],"class_list":["post-87689","post","type-post","status-publish","format-standard","hentry","category-upsc-nda-1","tag-1119","tag-mechanics","tag-physics","no-featured-image-padding"],"yoast_head":"\nSuppose there are two planets, 1 and 2, having the same density but th<\/title>\n<meta name=\"description\" content=\"If two planets have the same density but different radii R\u2081 and R\u2082 with R\u2081 > R\u2082, the acceleration due to gravity on the surface of the planet with the larger radius (Planet 1) will be greater than that on the surface of the planet with the smaller radius (Planet 2), i.e., g\u2081 > g\u2082. - The acceleration due to gravity on the surface of a sphere is given by g = GM\/R\u00b2, where G is the gravitational constant, M is the mass, and R is the radius. - The mass M can be expressed as M = \u03c1 * V, where \u03c1 is the density and V is the volume. For a sphere, V = (4\/3)\u03c0R\u00b3. - Substituting this into the gravity formula: g = G * (\u03c1 * (4\/3)\u03c0R\u00b3) \/ R\u00b2 = (4\/3)\u03c0G\u03c1R. - Since the density \u03c1 and constants G, 4\/3, and \u03c0 are the same for both planets, the acceleration due to gravity is directly proportional to the radius (g \u221d R). - Given R\u2081 > R\u2082, it follows that g\u2081 > g\u2082.\" \/>\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\/suppose-there-are-two-planets-1-and-2-having-the-same-density-but-th\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Suppose there are two planets, 1 and 2, having the same density but th\" \/>\n<meta property=\"og:description\" content=\"If two planets have the same density but different radii R\u2081 and R\u2082 with R\u2081 > R\u2082, the acceleration due to gravity on the surface of the planet with the larger radius (Planet 1) will be greater than that on the surface of the planet with the smaller radius (Planet 2), i.e., g\u2081 > g\u2082. - The acceleration due to gravity on the surface of a sphere is given by g = GM\/R\u00b2, where G is the gravitational constant, M is the mass, and R is the radius. - The mass M can be expressed as M = \u03c1 * V, where \u03c1 is the density and V is the volume. For a sphere, V = (4\/3)\u03c0R\u00b3. - Substituting this into the gravity formula: g = G * (\u03c1 * (4\/3)\u03c0R\u00b3) \/ R\u00b2 = (4\/3)\u03c0G\u03c1R. - Since the density \u03c1 and constants G, 4\/3, and \u03c0 are the same for both planets, the acceleration due to gravity is directly proportional to the radius (g \u221d R). - Given R\u2081 > R\u2082, it follows that g\u2081 > g\u2082.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/exam.pscnotes.com\/mcq\/suppose-there-are-two-planets-1-and-2-having-the-same-density-but-th\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ and Quiz for Exams\" \/>\n<meta property=\"article:published_time\" content=\"2025-06-01T06:51:18+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":"Suppose there are two planets, 1 and 2, having the same density but th","description":"If two planets have the same density but different radii R\u2081 and R\u2082 with R\u2081 > R\u2082, the acceleration due to gravity on the surface of the planet with the larger radius (Planet 1) will be greater than that on the surface of the planet with the smaller radius (Planet 2), i.e., g\u2081 > g\u2082. - The acceleration due to gravity on the surface of a sphere is given by g = GM\/R\u00b2, where G is the gravitational constant, M is the mass, and R is the radius. - The mass M can be expressed as M = \u03c1 * V, where \u03c1 is the density and V is the volume. For a sphere, V = (4\/3)\u03c0R\u00b3. - Substituting this into the gravity formula: g = G * (\u03c1 * (4\/3)\u03c0R\u00b3) \/ R\u00b2 = (4\/3)\u03c0G\u03c1R. - Since the density \u03c1 and constants G, 4\/3, and \u03c0 are the same for both planets, the acceleration due to gravity is directly proportional to the radius (g \u221d R). - Given R\u2081 > R\u2082, it follows that g\u2081 > g\u2082.","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\/suppose-there-are-two-planets-1-and-2-having-the-same-density-but-th\/","og_locale":"en_US","og_type":"article","og_title":"Suppose there are two planets, 1 and 2, having the same density but th","og_description":"If two planets have the same density but different radii R\u2081 and R\u2082 with R\u2081 > R\u2082, the acceleration due to gravity on the surface of the planet with the larger radius (Planet 1) will be greater than that on the surface of the planet with the smaller radius (Planet 2), i.e., g\u2081 > g\u2082. - The acceleration due to gravity on the surface of a sphere is given by g = GM\/R\u00b2, where G is the gravitational constant, M is the mass, and R is the radius. - The mass M can be expressed as M = \u03c1 * V, where \u03c1 is the density and V is the volume. For a sphere, V = (4\/3)\u03c0R\u00b3. - Substituting this into the gravity formula: g = G * (\u03c1 * (4\/3)\u03c0R\u00b3) \/ R\u00b2 = (4\/3)\u03c0G\u03c1R. - Since the density \u03c1 and constants G, 4\/3, and \u03c0 are the same for both planets, the acceleration due to gravity is directly proportional to the radius (g \u221d R). - Given R\u2081 > R\u2082, it follows that g\u2081 > g\u2082.","og_url":"https:\/\/exam.pscnotes.com\/mcq\/suppose-there-are-two-planets-1-and-2-having-the-same-density-but-th\/","og_site_name":"MCQ and Quiz for Exams","article_published_time":"2025-06-01T06:51:18+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\/suppose-there-are-two-planets-1-and-2-having-the-same-density-but-th\/","url":"https:\/\/exam.pscnotes.com\/mcq\/suppose-there-are-two-planets-1-and-2-having-the-same-density-but-th\/","name":"Suppose there are two planets, 1 and 2, having the same density but th","isPartOf":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#website"},"datePublished":"2025-06-01T06:51:18+00:00","dateModified":"2025-06-01T06:51:18+00:00","author":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209"},"description":"If two planets have the same density but different radii R\u2081 and R\u2082 with R\u2081 > R\u2082, the acceleration due to gravity on the surface of the planet with the larger radius (Planet 1) will be greater than that on the surface of the planet with the smaller radius (Planet 2), i.e., g\u2081 > g\u2082. - The acceleration due to gravity on the surface of a sphere is given by g = GM\/R\u00b2, where G is the gravitational constant, M is the mass, and R is the radius. - The mass M can be expressed as M = \u03c1 * V, where \u03c1 is the density and V is the volume. For a sphere, V = (4\/3)\u03c0R\u00b3. - Substituting this into the gravity formula: g = G * (\u03c1 * (4\/3)\u03c0R\u00b3) \/ R\u00b2 = (4\/3)\u03c0G\u03c1R. - Since the density \u03c1 and constants G, 4\/3, and \u03c0 are the same for both planets, the acceleration due to gravity is directly proportional to the radius (g \u221d R). - Given R\u2081 > R\u2082, it follows that g\u2081 > g\u2082.","breadcrumb":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/suppose-there-are-two-planets-1-and-2-having-the-same-density-but-th\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/exam.pscnotes.com\/mcq\/suppose-there-are-two-planets-1-and-2-having-the-same-density-but-th\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/exam.pscnotes.com\/mcq\/suppose-there-are-two-planets-1-and-2-having-the-same-density-but-th\/#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":"Suppose there are two planets, 1 and 2, having the same density but th"}]},{"@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\/87689","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=87689"}],"version-history":[{"count":0,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts\/87689\/revisions"}],"wp:attachment":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/media?parent=87689"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/categories?post=87689"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/tags?post=87689"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}