{"id":88542,"date":"2025-06-01T07:14:16","date_gmt":"2025-06-01T07:14:16","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=88542"},"modified":"2025-06-01T07:14:16","modified_gmt":"2025-06-01T07:14:16","slug":"a-solid-disc-and-a-solid-sphere-have-the-same-mass-and-same-radius-wh","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/a-solid-disc-and-a-solid-sphere-have-the-same-mass-and-same-radius-wh\/","title":{"rendered":"A solid disc and a solid sphere have the same mass and same radius. Wh"},"content":{"rendered":"

A solid disc and a solid sphere have the same mass and same radius. Which one has the higher moment of inertia about its centre of mass ?<\/p>\n

[amp_mcq option1=”The disc” option2=”The sphere” option3=”Both have the same moment of inertia” option4=”The information provided is not sufficient to answer the question” 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 moment of inertia ($I$) for a solid disc about an axis through its center and perpendicular to its plane is $I_{disc} = \\frac{1}{2}MR^2$. The moment of inertia for a solid sphere about an axis through its center is $I_{sphere} = \\frac{2}{5}MR^2$. Given that both the disc and the sphere have the same mass ($M$) and radius ($R$), we compare the coefficients $\\frac{1}{2}$ and $\\frac{2}{5}$. Since $\\frac{1}{2} = \\frac{5}{10}$ and $\\frac{2}{5} = \\frac{4}{10}$, we have $\\frac{1}{2} > \\frac{2}{5}$. Therefore, $I_{disc} > I_{sphere}$. The solid disc has the higher moment of inertia.
\n<\/section>\n
\n– Moment of inertia depends on the mass distribution relative to the axis of rotation.
\n– Formulas for the moment of inertia of common shapes are standard results derived from integration.
\n– For objects of the same mass and radius, the object with more mass distributed further from the axis of rotation will have a higher moment of inertia. In the disc, all mass is at a distance up to R from the axis in a plane, whereas in the sphere, mass is distributed in a volume, including closer to the center.
\n<\/section>\n
\n– Moment of inertia is a measure of an object’s resistance to changes in its rotational motion.
\n– A higher moment of inertia means it is harder to start or stop the rotation.
\n– The formulas used are for axes passing through the center of mass, as specified in the question.
\n<\/section>\n","protected":false},"excerpt":{"rendered":"

A solid disc and a solid sphere have the same mass and same radius. Which one has the higher moment of inertia about its centre of mass ? [amp_mcq option1=”The disc” option2=”The sphere” option3=”Both have the same moment of inertia” option4=”The information provided is not sufficient to answer the question” correct=”option1″] This question was previously … <\/p>\n

Detailed SolutionA solid disc and a solid sphere have the same mass and same radius. Wh<\/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-88542","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 solid disc and a solid sphere have the same mass and same radius. Wh<\/title>\n<meta name=\"description\" content=\"The moment of inertia ($I$) for a solid disc about an axis through its center and perpendicular to its plane is $I_{disc} = frac{1}{2}MR^2$. The moment of inertia for a solid sphere about an axis through its center is $I_{sphere} = frac{2}{5}MR^2$. Given that both the disc and the sphere have the same mass ($M$) and radius ($R$), we compare the coefficients $frac{1}{2}$ and $frac{2}{5}$. Since $frac{1}{2} = frac{5}{10}$ and $frac{2}{5} = frac{4}{10}$, we have $frac{1}{2} > frac{2}{5}$. Therefore, $I_{disc} > I_{sphere}$. The solid disc has the higher moment of inertia. - Moment of inertia depends on the mass distribution relative to the axis of rotation. - Formulas for the moment of inertia of common shapes are standard results derived from integration. - For objects of the same mass and radius, the object with more mass distributed further from the axis of rotation will have a higher moment of inertia. In the disc, all mass is at a distance up to R from the axis in a plane, whereas in the sphere, mass is distributed in a volume, including closer to the center.\" \/>\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-solid-disc-and-a-solid-sphere-have-the-same-mass-and-same-radius-wh\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"A solid disc and a solid sphere have the same mass and same radius. Wh\" \/>\n<meta property=\"og:description\" content=\"The moment of inertia ($I$) for a solid disc about an axis through its center and perpendicular to its plane is $I_{disc} = frac{1}{2}MR^2$. The moment of inertia for a solid sphere about an axis through its center is $I_{sphere} = frac{2}{5}MR^2$. Given that both the disc and the sphere have the same mass ($M$) and radius ($R$), we compare the coefficients $frac{1}{2}$ and $frac{2}{5}$. Since $frac{1}{2} = frac{5}{10}$ and $frac{2}{5} = frac{4}{10}$, we have $frac{1}{2} > frac{2}{5}$. Therefore, $I_{disc} > I_{sphere}$. The solid disc has the higher moment of inertia. - Moment of inertia depends on the mass distribution relative to the axis of rotation. - Formulas for the moment of inertia of common shapes are standard results derived from integration. - For objects of the same mass and radius, the object with more mass distributed further from the axis of rotation will have a higher moment of inertia. In the disc, all mass is at a distance up to R from the axis in a plane, whereas in the sphere, mass is distributed in a volume, including closer to the center.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/exam.pscnotes.com\/mcq\/a-solid-disc-and-a-solid-sphere-have-the-same-mass-and-same-radius-wh\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ and Quiz for Exams\" \/>\n<meta property=\"article:published_time\" content=\"2025-06-01T07:14:16+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=\"2 minutes\" \/>\n<!-- \/ Yoast SEO Premium plugin. -->","yoast_head_json":{"title":"A solid disc and a solid sphere have the same mass and same radius. Wh","description":"The moment of inertia ($I$) for a solid disc about an axis through its center and perpendicular to its plane is $I_{disc} = frac{1}{2}MR^2$. The moment of inertia for a solid sphere about an axis through its center is $I_{sphere} = frac{2}{5}MR^2$. Given that both the disc and the sphere have the same mass ($M$) and radius ($R$), we compare the coefficients $frac{1}{2}$ and $frac{2}{5}$. Since $frac{1}{2} = frac{5}{10}$ and $frac{2}{5} = frac{4}{10}$, we have $frac{1}{2} > frac{2}{5}$. Therefore, $I_{disc} > I_{sphere}$. The solid disc has the higher moment of inertia. - Moment of inertia depends on the mass distribution relative to the axis of rotation. - Formulas for the moment of inertia of common shapes are standard results derived from integration. - For objects of the same mass and radius, the object with more mass distributed further from the axis of rotation will have a higher moment of inertia. In the disc, all mass is at a distance up to R from the axis in a plane, whereas in the sphere, mass is distributed in a volume, including closer to the center.","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-solid-disc-and-a-solid-sphere-have-the-same-mass-and-same-radius-wh\/","og_locale":"en_US","og_type":"article","og_title":"A solid disc and a solid sphere have the same mass and same radius. Wh","og_description":"The moment of inertia ($I$) for a solid disc about an axis through its center and perpendicular to its plane is $I_{disc} = frac{1}{2}MR^2$. The moment of inertia for a solid sphere about an axis through its center is $I_{sphere} = frac{2}{5}MR^2$. Given that both the disc and the sphere have the same mass ($M$) and radius ($R$), we compare the coefficients $frac{1}{2}$ and $frac{2}{5}$. Since $frac{1}{2} = frac{5}{10}$ and $frac{2}{5} = frac{4}{10}$, we have $frac{1}{2} > frac{2}{5}$. Therefore, $I_{disc} > I_{sphere}$. The solid disc has the higher moment of inertia. - Moment of inertia depends on the mass distribution relative to the axis of rotation. - Formulas for the moment of inertia of common shapes are standard results derived from integration. - For objects of the same mass and radius, the object with more mass distributed further from the axis of rotation will have a higher moment of inertia. In the disc, all mass is at a distance up to R from the axis in a plane, whereas in the sphere, mass is distributed in a volume, including closer to the center.","og_url":"https:\/\/exam.pscnotes.com\/mcq\/a-solid-disc-and-a-solid-sphere-have-the-same-mass-and-same-radius-wh\/","og_site_name":"MCQ and Quiz for Exams","article_published_time":"2025-06-01T07:14:16+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-solid-disc-and-a-solid-sphere-have-the-same-mass-and-same-radius-wh\/","url":"https:\/\/exam.pscnotes.com\/mcq\/a-solid-disc-and-a-solid-sphere-have-the-same-mass-and-same-radius-wh\/","name":"A solid disc and a solid sphere have the same mass and same radius. Wh","isPartOf":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#website"},"datePublished":"2025-06-01T07:14:16+00:00","dateModified":"2025-06-01T07:14:16+00:00","author":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209"},"description":"The moment of inertia ($I$) for a solid disc about an axis through its center and perpendicular to its plane is $I_{disc} = \\frac{1}{2}MR^2$. The moment of inertia for a solid sphere about an axis through its center is $I_{sphere} = \\frac{2}{5}MR^2$. Given that both the disc and the sphere have the same mass ($M$) and radius ($R$), we compare the coefficients $\\frac{1}{2}$ and $\\frac{2}{5}$. Since $\\frac{1}{2} = \\frac{5}{10}$ and $\\frac{2}{5} = \\frac{4}{10}$, we have $\\frac{1}{2} > \\frac{2}{5}$. Therefore, $I_{disc} > I_{sphere}$. The solid disc has the higher moment of inertia. - Moment of inertia depends on the mass distribution relative to the axis of rotation. - Formulas for the moment of inertia of common shapes are standard results derived from integration. - For objects of the same mass and radius, the object with more mass distributed further from the axis of rotation will have a higher moment of inertia. 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