{"id":87932,"date":"2025-06-01T06:58:05","date_gmt":"2025-06-01T06:58:05","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=87932"},"modified":"2025-06-01T06:58:05","modified_gmt":"2025-06-01T06:58:05","slug":"a-sphere-of-volume-v-is-made-of-a-material-with-lower-density-than-wat","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/a-sphere-of-volume-v-is-made-of-a-material-with-lower-density-than-wat\/","title":{"rendered":"A sphere of volume V is made of a material with lower density than wat"},"content":{"rendered":"

A sphere of volume V is made of a material with lower density than water. While on Earth, it floats on water with its volume f\u2081V (f\u2081 < 1) submerged. On the other hand, on a spaceship accelerating with acceleration a < g (g is the acceleration due to gravity on Earth) in outer space, its submerged volume in water is f\u2082V. Then:\n\n[amp_mcq option1=\"f\u2082=f\u2081\" option2=\"f\u2082 = (a\/g) * f\u2081\" option3=\"f\u2082 > f\u2081” option4=”f\u2082 = (g\/(g-a)) * f\u2081” correct=”option1″]<\/p>\n

\n
\n
This question was previously asked in<\/div>\n
UPSC NDA-1 – 2023<\/div>\n<\/div>\n
Download PDF<\/a>Attempt Online<\/a><\/div>\n<\/div>\n
\nThe correct option is A.
\n<\/section>\n
\nThe fraction of volume submerged when an object floats in a fluid is determined by the ratio of the object’s density to the fluid’s density ($f = \\rho_{object} \/ \\rho_{fluid}$). This relationship arises from the condition that the buoyant force equals the weight of the object. Both the buoyant force (which depends on the effective acceleration) and the weight (which also depends on the effective acceleration) are directly proportional to the effective acceleration. Therefore, the ratio of densities, and hence the fraction of submerged volume, is independent of the magnitude of the uniform effective acceleration (like gravity) acting on the system.
\n<\/section>\n
\nOn Earth, the buoyant force is $F_{B1} = \\rho_w (f_1V) g$ and the weight is $W_1 = \\rho_s V g$. Since it floats, $F_{B1} = W_1 \\implies \\rho_w f_1 V g = \\rho_s V g \\implies f_1 = \\rho_s \/ \\rho_w$. On the spaceship with effective acceleration $a$, the buoyant force is $F_{B2} = \\rho_w (f_2V) a$ and the weight is $W_2 = \\rho_s V a$. Since it floats, $F_{B2} = W_2 \\implies \\rho_w f_2 V a = \\rho_s V a \\implies f_2 = \\rho_s \/ \\rho_w$. Thus, $f_1 = f_2$. The magnitude of the effective acceleration affects the magnitude of the forces but not their ratio when determining the submerged fraction.
\n<\/section>\n","protected":false},"excerpt":{"rendered":"

A sphere of volume V is made of a material with lower density than water. While on Earth, it floats on water with its volume f\u2081V (f\u2081 < 1) submerged. On the other hand, on a spaceship accelerating with acceleration a < g (g is the acceleration due to gravity on Earth) in outer space, ... \n\n

Detailed SolutionA sphere of volume V is made of a material with lower density than wat<\/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":[1105,1129,1128],"class_list":["post-87932","post","type-post","status-publish","format-standard","hentry","category-upsc-nda-1","tag-1105","tag-mechanics","tag-physics","no-featured-image-padding"],"yoast_head":"\nA sphere of volume V is made of a material with lower density than wat<\/title>\n<meta name=\"description\" content=\"The correct option is A. The fraction of volume submerged when an object floats in a fluid is determined by the ratio of the object's density to the fluid's density ($f = rho_{object} \/ rho_{fluid}$). This relationship arises from the condition that the buoyant force equals the weight of the object. Both the buoyant force (which depends on the effective acceleration) and the weight (which also depends on the effective acceleration) are directly proportional to the effective acceleration. Therefore, the ratio of densities, and hence the fraction of submerged volume, is independent of the magnitude of the uniform effective acceleration (like gravity) acting on the system.\" \/>\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-sphere-of-volume-v-is-made-of-a-material-with-lower-density-than-wat\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"A sphere of volume V is made of a material with lower density than wat\" \/>\n<meta property=\"og:description\" content=\"The correct option is A. The fraction of volume submerged when an object floats in a fluid is determined by the ratio of the object's density to the fluid's density ($f = rho_{object} \/ rho_{fluid}$). This relationship arises from the condition that the buoyant force equals the weight of the object. Both the buoyant force (which depends on the effective acceleration) and the weight (which also depends on the effective acceleration) are directly proportional to the effective acceleration. Therefore, the ratio of densities, and hence the fraction of submerged volume, is independent of the magnitude of the uniform effective acceleration (like gravity) acting on the system.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/exam.pscnotes.com\/mcq\/a-sphere-of-volume-v-is-made-of-a-material-with-lower-density-than-wat\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ and Quiz for Exams\" \/>\n<meta property=\"article:published_time\" content=\"2025-06-01T06:58:05+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=\"2 minutes\" \/>\n<!-- \/ Yoast SEO Premium plugin. -->","yoast_head_json":{"title":"A sphere of volume V is made of a material with lower density than wat","description":"The correct option is A. The fraction of volume submerged when an object floats in a fluid is determined by the ratio of the object's density to the fluid's density ($f = rho_{object} \/ rho_{fluid}$). This relationship arises from the condition that the buoyant force equals the weight of the object. Both the buoyant force (which depends on the effective acceleration) and the weight (which also depends on the effective acceleration) are directly proportional to the effective acceleration. Therefore, the ratio of densities, and hence the fraction of submerged volume, is independent of the magnitude of the uniform effective acceleration (like gravity) acting on the system.","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-sphere-of-volume-v-is-made-of-a-material-with-lower-density-than-wat\/","og_locale":"en_US","og_type":"article","og_title":"A sphere of volume V is made of a material with lower density than wat","og_description":"The correct option is A. The fraction of volume submerged when an object floats in a fluid is determined by the ratio of the object's density to the fluid's density ($f = rho_{object} \/ rho_{fluid}$). This relationship arises from the condition that the buoyant force equals the weight of the object. Both the buoyant force (which depends on the effective acceleration) and the weight (which also depends on the effective acceleration) are directly proportional to the effective acceleration. Therefore, the ratio of densities, and hence the fraction of submerged volume, is independent of the magnitude of the uniform effective acceleration (like gravity) acting on the system.","og_url":"https:\/\/exam.pscnotes.com\/mcq\/a-sphere-of-volume-v-is-made-of-a-material-with-lower-density-than-wat\/","og_site_name":"MCQ and Quiz for Exams","article_published_time":"2025-06-01T06:58:05+00:00","author":"rawan239","twitter_card":"summary_large_image","twitter_misc":{"Written by":"rawan239","Est. reading time":"2 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/exam.pscnotes.com\/mcq\/a-sphere-of-volume-v-is-made-of-a-material-with-lower-density-than-wat\/","url":"https:\/\/exam.pscnotes.com\/mcq\/a-sphere-of-volume-v-is-made-of-a-material-with-lower-density-than-wat\/","name":"A sphere of volume V is made of a material with lower density than wat","isPartOf":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#website"},"datePublished":"2025-06-01T06:58:05+00:00","dateModified":"2025-06-01T06:58:05+00:00","author":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209"},"description":"The correct option is A. The fraction of volume submerged when an object floats in a fluid is determined by the ratio of the object's density to the fluid's density ($f = \\rho_{object} \/ \\rho_{fluid}$). This relationship arises from the condition that the buoyant force equals the weight of the object. Both the buoyant force (which depends on the effective acceleration) and the weight (which also depends on the effective acceleration) are directly proportional to the effective acceleration. Therefore, the ratio of densities, and hence the fraction of submerged volume, is independent of the magnitude of the uniform effective acceleration (like gravity) acting on the system.","breadcrumb":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/a-sphere-of-volume-v-is-made-of-a-material-with-lower-density-than-wat\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/exam.pscnotes.com\/mcq\/a-sphere-of-volume-v-is-made-of-a-material-with-lower-density-than-wat\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/exam.pscnotes.com\/mcq\/a-sphere-of-volume-v-is-made-of-a-material-with-lower-density-than-wat\/#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 sphere of volume V is made of a material with lower density than wat"}]},{"@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\/87932","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=87932"}],"version-history":[{"count":0,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts\/87932\/revisions"}],"wp:attachment":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/media?parent=87932"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/categories?post=87932"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/tags?post=87932"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}