{"id":87166,"date":"2025-06-01T04:30:29","date_gmt":"2025-06-01T04:30:29","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=87166"},"modified":"2025-06-01T04:30:29","modified_gmt":"2025-06-01T04:30:29","slug":"a-planar-irregular-shaped-object-has-a-mass-of-2-kg-its-moment-of-in","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/a-planar-irregular-shaped-object-has-a-mass-of-2-kg-its-moment-of-in\/","title":{"rendered":"A planar, irregular shaped object has a mass of 2 kg. Its moment of in"},"content":{"rendered":"

A planar, irregular shaped object has a mass of 2 kg. Its moment of inertia along the two orthogonal axes in the plane of the object are 3 kg m\u00b2 and 4 kg m\u00b2, respectively. The moment of inertia of the object along an axis perpendicular to the plane and passing through a point 0\u00b75 m away from its centre of mass is represented by I. Which one among the following is the correct value of I ?<\/p>\n

[amp_mcq option1=”7\u00b75 kg m\u00b2” option2=”7 kg m\u00b2” option3=”5 kg m\u00b2” option4=”1 kg m\u00b2” correct=”option1″]<\/p>\n

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This question was previously asked in<\/div>\n
UPSC Geoscientist – 2024<\/div>\n<\/div>\n
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\nFor a planar object, the moment of inertia about an axis perpendicular to the plane and passing through a point is related to the moments of inertia about two perpendicular axes in the plane by the perpendicular axis theorem and the parallel axis theorem.
\n<\/section>\n
\nBy the perpendicular axis theorem, the moment of inertia about the center of mass (assuming the given orthogonal axes intersect at CM) and perpendicular to the plane is I_CM = Ix + Iy = 3 kg m\u00b2 + 4 kg m\u00b2 = 7 kg m\u00b2. By the parallel axis theorem, the moment of inertia I about a parallel axis perpendicular to the plane and at a distance d = 0.5 m from CM is I = I_CM + m d\u00b2.
\n<\/section>\n
\nGiven mass m = 2 kg and distance d = 0.5 m. I = 7 kg m\u00b2 + (2 kg)(0.5 m)\u00b2 = 7 + 2(0.25) = 7 + 0.5 = 7.5 kg m\u00b2.
\n<\/section>\n","protected":false},"excerpt":{"rendered":"

A planar, irregular shaped object has a mass of 2 kg. Its moment of inertia along the two orthogonal axes in the plane of the object are 3 kg m\u00b2 and 4 kg m\u00b2, respectively. The moment of inertia of the object along an axis perpendicular to the plane and passing through a point 0\u00b75 … <\/p>\n

Detailed SolutionA planar, irregular shaped object has a mass of 2 kg. Its moment of in<\/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":[1091],"tags":[1103,1129,1128],"class_list":["post-87166","post","type-post","status-publish","format-standard","hentry","category-upsc-geoscientist","tag-1103","tag-mechanics","tag-physics","no-featured-image-padding"],"yoast_head":"\nA planar, irregular shaped object has a mass of 2 kg. Its moment of in<\/title>\n<meta name=\"description\" content=\"For a planar object, the moment of inertia about an axis perpendicular to the plane and passing through a point is related to the moments of inertia about two perpendicular axes in the plane by the perpendicular axis theorem and the parallel axis theorem. By the perpendicular axis theorem, the moment of inertia about the center of mass (assuming the given orthogonal axes intersect at CM) and perpendicular to the plane is I_CM = Ix + Iy = 3 kg m\u00b2 + 4 kg m\u00b2 = 7 kg m\u00b2. By the parallel axis theorem, the moment of inertia I about a parallel axis perpendicular to the plane and at a distance d = 0.5 m from CM is I = I_CM + m d\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-planar-irregular-shaped-object-has-a-mass-of-2-kg-its-moment-of-in\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"A planar, irregular shaped object has a mass of 2 kg. Its moment of in\" \/>\n<meta property=\"og:description\" content=\"For a planar object, the moment of inertia about an axis perpendicular to the plane and passing through a point is related to the moments of inertia about two perpendicular axes in the plane by the perpendicular axis theorem and the parallel axis theorem. By the perpendicular axis theorem, the moment of inertia about the center of mass (assuming the given orthogonal axes intersect at CM) and perpendicular to the plane is I_CM = Ix + Iy = 3 kg m\u00b2 + 4 kg m\u00b2 = 7 kg m\u00b2. By the parallel axis theorem, the moment of inertia I about a parallel axis perpendicular to the plane and at a distance d = 0.5 m from CM is I = I_CM + m d\u00b2.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/exam.pscnotes.com\/mcq\/a-planar-irregular-shaped-object-has-a-mass-of-2-kg-its-moment-of-in\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ and Quiz for Exams\" \/>\n<meta property=\"article:published_time\" content=\"2025-06-01T04:30:29+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":"A planar, irregular shaped object has a mass of 2 kg. Its moment of in","description":"For a planar object, the moment of inertia about an axis perpendicular to the plane and passing through a point is related to the moments of inertia about two perpendicular axes in the plane by the perpendicular axis theorem and the parallel axis theorem. By the perpendicular axis theorem, the moment of inertia about the center of mass (assuming the given orthogonal axes intersect at CM) and perpendicular to the plane is I_CM = Ix + Iy = 3 kg m\u00b2 + 4 kg m\u00b2 = 7 kg m\u00b2. By the parallel axis theorem, the moment of inertia I about a parallel axis perpendicular to the plane and at a distance d = 0.5 m from CM is I = I_CM + m d\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-planar-irregular-shaped-object-has-a-mass-of-2-kg-its-moment-of-in\/","og_locale":"en_US","og_type":"article","og_title":"A planar, irregular shaped object has a mass of 2 kg. Its moment of in","og_description":"For a planar object, the moment of inertia about an axis perpendicular to the plane and passing through a point is related to the moments of inertia about two perpendicular axes in the plane by the perpendicular axis theorem and the parallel axis theorem. By the perpendicular axis theorem, the moment of inertia about the center of mass (assuming the given orthogonal axes intersect at CM) and perpendicular to the plane is I_CM = Ix + Iy = 3 kg m\u00b2 + 4 kg m\u00b2 = 7 kg m\u00b2. By the parallel axis theorem, the moment of inertia I about a parallel axis perpendicular to the plane and at a distance d = 0.5 m from CM is I = I_CM + m d\u00b2.","og_url":"https:\/\/exam.pscnotes.com\/mcq\/a-planar-irregular-shaped-object-has-a-mass-of-2-kg-its-moment-of-in\/","og_site_name":"MCQ and Quiz for Exams","article_published_time":"2025-06-01T04:30:29+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\/a-planar-irregular-shaped-object-has-a-mass-of-2-kg-its-moment-of-in\/","url":"https:\/\/exam.pscnotes.com\/mcq\/a-planar-irregular-shaped-object-has-a-mass-of-2-kg-its-moment-of-in\/","name":"A planar, irregular shaped object has a mass of 2 kg. 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