{"id":88529,"date":"2025-06-01T07:14:02","date_gmt":"2025-06-01T07:14:02","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=88529"},"modified":"2025-06-01T07:14:02","modified_gmt":"2025-06-01T07:14:02","slug":"a-thin-disc-and-a-thin-ring-both-have-mass-m-and-radius-r-both-rotat","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/a-thin-disc-and-a-thin-ring-both-have-mass-m-and-radius-r-both-rotat\/","title":{"rendered":"A thin disc and a thin ring, both have mass M and radius R. Both rotat"},"content":{"rendered":"

A thin disc and a thin ring, both have mass M and radius R. Both rotate about axes through their center of mass and are perpendicular to their surfaces at the same angular velocity. Which of the following is true ?<\/p>\n

[amp_mcq option1=”The ring has higher kinetic energy” option2=”The disc has higher kinetic energy” option3=”The ring and the disc have the same kinetic energy” option4=”Kinetic energies of both the bodies are zero since they are not in linear motion” correct=”option1″]<\/p>\n

\n
\n
This question was previously asked in<\/div>\n
UPSC NDA-2 – 2019<\/div>\n<\/div>\n
Download PDF<\/a>Attempt Online<\/a><\/div>\n<\/div>\n
\nThe correct option is A) The ring has higher kinetic energy. The rotational kinetic energy is given by KE = (1\/2) * I * \u03c9\u00b2, where I is the moment of inertia and \u03c9 is the angular velocity. Since both the ring and the disc have the same mass (M) and radius (R) and rotate at the same angular velocity (\u03c9), the kinetic energy depends on their moments of inertia.
\n<\/section>\n
\nThe moment of inertia of a thin ring about an axis through its center and perpendicular to its plane is I_ring = M * R\u00b2. The moment of inertia of a thin disc about an axis through its center and perpendicular to its plane is I_disc = (1\/2) * M * R\u00b2. Since I_ring > I_disc (M*R\u00b2 is greater than (1\/2)*M*R\u00b2), and \u03c9 is the same for both, the rotational kinetic energy of the ring is higher than that of the disc (KE_ring = (1\/2)*I_ring*\u03c9\u00b2 > KE_disc = (1\/2)*I_disc*\u03c9\u00b2).
\n<\/section>\n
\nMoment of inertia represents the resistance of an object to rotational motion; it depends on the mass distribution relative to the axis of rotation. For the same total mass and radius, the ring has mass distributed further from the axis (all at radius R) compared to the disc (mass distributed from center to R), resulting in a higher moment of inertia for the ring. Kinetic energy of a body rotating is non-zero unless its angular velocity is zero, so option D is incorrect.
\n<\/section>\n","protected":false},"excerpt":{"rendered":"

A thin disc and a thin ring, both have mass M and radius R. Both rotate about axes through their center of mass and are perpendicular to their surfaces at the same angular velocity. Which of the following is true ? [amp_mcq option1=”The ring has higher kinetic energy” option2=”The disc has higher kinetic energy” option3=”The … <\/p>\n

Detailed SolutionA thin disc and a thin ring, both have mass M and radius R. Both rotat<\/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":[1119,1129,1128],"class_list":["post-88529","post","type-post","status-publish","format-standard","hentry","category-upsc-nda-2","tag-1119","tag-mechanics","tag-physics","no-featured-image-padding"],"yoast_head":"\nA thin disc and a thin ring, both have mass M and radius R. Both rotat<\/title>\n<meta name=\"description\" content=\"The correct option is A) The ring has higher kinetic energy. The rotational kinetic energy is given by KE = (1\/2) * I * \u03c9\u00b2, where I is the moment of inertia and \u03c9 is the angular velocity. Since both the ring and the disc have the same mass (M) and radius (R) and rotate at the same angular velocity (\u03c9), the kinetic energy depends on their moments of inertia. The moment of inertia of a thin ring about an axis through its center and perpendicular to its plane is I_ring = M * R\u00b2. The moment of inertia of a thin disc about an axis through its center and perpendicular to its plane is I_disc = (1\/2) * M * R\u00b2. Since I_ring > I_disc (M*R\u00b2 is greater than (1\/2)*M*R\u00b2), and \u03c9 is the same for both, the rotational kinetic energy of the ring is higher than that of the disc (KE_ring = (1\/2)*I_ring*\u03c9\u00b2 > KE_disc = (1\/2)*I_disc*\u03c9\u00b2).\" \/>\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-thin-disc-and-a-thin-ring-both-have-mass-m-and-radius-r-both-rotat\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"A thin disc and a thin ring, both have mass M and radius R. Both rotat\" \/>\n<meta property=\"og:description\" content=\"The correct option is A) The ring has higher kinetic energy. The rotational kinetic energy is given by KE = (1\/2) * I * \u03c9\u00b2, where I is the moment of inertia and \u03c9 is the angular velocity. Since both the ring and the disc have the same mass (M) and radius (R) and rotate at the same angular velocity (\u03c9), the kinetic energy depends on their moments of inertia. The moment of inertia of a thin ring about an axis through its center and perpendicular to its plane is I_ring = M * R\u00b2. The moment of inertia of a thin disc about an axis through its center and perpendicular to its plane is I_disc = (1\/2) * M * R\u00b2. Since I_ring > I_disc (M*R\u00b2 is greater than (1\/2)*M*R\u00b2), and \u03c9 is the same for both, the rotational kinetic energy of the ring is higher than that of the disc (KE_ring = (1\/2)*I_ring*\u03c9\u00b2 > KE_disc = (1\/2)*I_disc*\u03c9\u00b2).\" \/>\n<meta property=\"og:url\" content=\"https:\/\/exam.pscnotes.com\/mcq\/a-thin-disc-and-a-thin-ring-both-have-mass-m-and-radius-r-both-rotat\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ and Quiz for Exams\" \/>\n<meta property=\"article:published_time\" content=\"2025-06-01T07:14:02+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 thin disc and a thin ring, both have mass M and radius R. Both rotat","description":"The correct option is A) The ring has higher kinetic energy. The rotational kinetic energy is given by KE = (1\/2) * I * \u03c9\u00b2, where I is the moment of inertia and \u03c9 is the angular velocity. Since both the ring and the disc have the same mass (M) and radius (R) and rotate at the same angular velocity (\u03c9), the kinetic energy depends on their moments of inertia. The moment of inertia of a thin ring about an axis through its center and perpendicular to its plane is I_ring = M * R\u00b2. The moment of inertia of a thin disc about an axis through its center and perpendicular to its plane is I_disc = (1\/2) * M * R\u00b2. Since I_ring > I_disc (M*R\u00b2 is greater than (1\/2)*M*R\u00b2), and \u03c9 is the same for both, the rotational kinetic energy of the ring is higher than that of the disc (KE_ring = (1\/2)*I_ring*\u03c9\u00b2 > KE_disc = (1\/2)*I_disc*\u03c9\u00b2).","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-thin-disc-and-a-thin-ring-both-have-mass-m-and-radius-r-both-rotat\/","og_locale":"en_US","og_type":"article","og_title":"A thin disc and a thin ring, both have mass M and radius R. Both rotat","og_description":"The correct option is A) The ring has higher kinetic energy. The rotational kinetic energy is given by KE = (1\/2) * I * \u03c9\u00b2, where I is the moment of inertia and \u03c9 is the angular velocity. Since both the ring and the disc have the same mass (M) and radius (R) and rotate at the same angular velocity (\u03c9), the kinetic energy depends on their moments of inertia. The moment of inertia of a thin ring about an axis through its center and perpendicular to its plane is I_ring = M * R\u00b2. The moment of inertia of a thin disc about an axis through its center and perpendicular to its plane is I_disc = (1\/2) * M * R\u00b2. Since I_ring > I_disc (M*R\u00b2 is greater than (1\/2)*M*R\u00b2), and \u03c9 is the same for both, the rotational kinetic energy of the ring is higher than that of the disc (KE_ring = (1\/2)*I_ring*\u03c9\u00b2 > KE_disc = (1\/2)*I_disc*\u03c9\u00b2).","og_url":"https:\/\/exam.pscnotes.com\/mcq\/a-thin-disc-and-a-thin-ring-both-have-mass-m-and-radius-r-both-rotat\/","og_site_name":"MCQ and Quiz for Exams","article_published_time":"2025-06-01T07:14:02+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-thin-disc-and-a-thin-ring-both-have-mass-m-and-radius-r-both-rotat\/","url":"https:\/\/exam.pscnotes.com\/mcq\/a-thin-disc-and-a-thin-ring-both-have-mass-m-and-radius-r-both-rotat\/","name":"A thin disc and a thin ring, both have mass M and radius R. Both rotat","isPartOf":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#website"},"datePublished":"2025-06-01T07:14:02+00:00","dateModified":"2025-06-01T07:14:02+00:00","author":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209"},"description":"The correct option is A) The ring has higher kinetic energy. The rotational kinetic energy is given by KE = (1\/2) * I * \u03c9\u00b2, where I is the moment of inertia and \u03c9 is the angular velocity. Since both the ring and the disc have the same mass (M) and radius (R) and rotate at the same angular velocity (\u03c9), the kinetic energy depends on their moments of inertia. The moment of inertia of a thin ring about an axis through its center and perpendicular to its plane is I_ring = M * R\u00b2. The moment of inertia of a thin disc about an axis through its center and perpendicular to its plane is I_disc = (1\/2) * M * R\u00b2. Since I_ring > I_disc (M*R\u00b2 is greater than (1\/2)*M*R\u00b2), and \u03c9 is the same for both, the rotational kinetic energy of the ring is higher than that of the disc (KE_ring = (1\/2)*I_ring*\u03c9\u00b2 > KE_disc = (1\/2)*I_disc*\u03c9\u00b2).","breadcrumb":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/a-thin-disc-and-a-thin-ring-both-have-mass-m-and-radius-r-both-rotat\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/exam.pscnotes.com\/mcq\/a-thin-disc-and-a-thin-ring-both-have-mass-m-and-radius-r-both-rotat\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/exam.pscnotes.com\/mcq\/a-thin-disc-and-a-thin-ring-both-have-mass-m-and-radius-r-both-rotat\/#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":"A thin disc and a thin ring, both have mass M and radius R. Both rotat"}]},{"@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\/88529","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=88529"}],"version-history":[{"count":0,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts\/88529\/revisions"}],"wp:attachment":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/media?parent=88529"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/categories?post=88529"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/tags?post=88529"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}