{"id":89957,"date":"2025-06-01T10:17:56","date_gmt":"2025-06-01T10:17:56","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=89957"},"modified":"2025-06-01T10:17:56","modified_gmt":"2025-06-01T10:17:56","slug":"two-racing-cars-of-masses-m%e2%82%81-and-m%e2%82%82-are-moving-in-circles-of-radii-r%e2%82%81","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/two-racing-cars-of-masses-m%e2%82%81-and-m%e2%82%82-are-moving-in-circles-of-radii-r%e2%82%81\/","title":{"rendered":"Two racing cars of masses m\u2081 and m\u2082 are moving in circles of radii r\u2081"},"content":{"rendered":"

Two racing cars of masses m\u2081 and m\u2082 are moving in circles of radii r\u2081 and r\u2082 respectively. Their speeds are such that each car makes a complete circle in the same time ‘t’. The ratio of angular speed of the first to that of the second car is :<\/p>\n

[amp_mcq option1=”m\u2081 : m\u2082” option2=”1 : 1″ option3=”r\u2081 : r\u2082” option4=”1 : 2″ correct=”option2″]<\/p>\n

\n
\n
This question was previously asked in<\/div>\n
UPSC CAPF – 2015<\/div>\n<\/div>\n
Download PDF<\/a>Attempt Online<\/a><\/div>\n<\/div>\n
\nThe correct answer is 1 : 1.
\n<\/section>\n
\nAngular speed (\u03c9) is defined as the rate of change of angular displacement. For an object moving in a circle, the angular speed is given by \u03c9 = 2\u03c0 \/ T, where T is the time period (time taken to complete one revolution). The problem states that both cars make a complete circle in the same time ‘t’. Therefore, the time period T is the same for both cars.
\nFor the first car, \u03c9\u2081 = 2\u03c0 \/ t.
\nFor the second car, \u03c9\u2082 = 2\u03c0 \/ t.
\nThe ratio of their angular speeds is \u03c9\u2081 : \u03c9\u2082 = (2\u03c0 \/ t) : (2\u03c0 \/ t) = 1 : 1.
\nThe masses (m\u2081 and m\u2082) and radii (r\u2081 and r\u2082) of the cars are irrelevant for determining the ratio of angular speeds when the time period is given to be the same.
\n<\/section>\n
\nLinear speed (v) is related to angular speed and radius by v = r\u03c9. If the angular speeds are the same but the radii are different, the linear speeds will be different. Centripetal acceleration (a_c = r\u03c9\u00b2) and centripetal force (F_c = m a_c = m r\u03c9\u00b2) would also depend on the mass and radius even if the angular speed is constant. This question specifically asks for the ratio of angular speed, which is determined solely by the time period in this case.
\n<\/section>\n","protected":false},"excerpt":{"rendered":"

Two racing cars of masses m\u2081 and m\u2082 are moving in circles of radii r\u2081 and r\u2082 respectively. Their speeds are such that each car makes a complete circle in the same time ‘t’. The ratio of angular speed of the first to that of the second car is : [amp_mcq option1=”m\u2081 : m\u2082” option2=”1 … <\/p>\n

Detailed SolutionTwo racing cars of masses m\u2081 and m\u2082 are moving in circles of radii r\u2081<\/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":[1085],"tags":[1443,1129,1128],"class_list":["post-89957","post","type-post","status-publish","format-standard","hentry","category-upsc-capf","tag-1443","tag-mechanics","tag-physics","no-featured-image-padding"],"yoast_head":"\nTwo racing cars of masses m\u2081 and m\u2082 are moving in circles of radii r\u2081<\/title>\n<meta name=\"description\" content=\"The correct answer is 1 : 1. Angular speed (\u03c9) is defined as the rate of change of angular displacement. For an object moving in a circle, the angular speed is given by \u03c9 = 2\u03c0 \/ T, where T is the time period (time taken to complete one revolution). The problem states that both cars make a complete circle in the same time 't'. Therefore, the time period T is the same for both cars. For the first car, \u03c9\u2081 = 2\u03c0 \/ t. For the second car, \u03c9\u2082 = 2\u03c0 \/ t. The ratio of their angular speeds is \u03c9\u2081 : \u03c9\u2082 = (2\u03c0 \/ t) : (2\u03c0 \/ t) = 1 : 1. The masses (m\u2081 and m\u2082) and radii (r\u2081 and r\u2082) of the cars are irrelevant for determining the ratio of angular speeds when the time period is given to be the same.\" \/>\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\/two-racing-cars-of-masses-m\u2081-and-m\u2082-are-moving-in-circles-of-radii-r\u2081\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Two racing cars of masses m\u2081 and m\u2082 are moving in circles of radii r\u2081\" \/>\n<meta property=\"og:description\" content=\"The correct answer is 1 : 1. Angular speed (\u03c9) is defined as the rate of change of angular displacement. For an object moving in a circle, the angular speed is given by \u03c9 = 2\u03c0 \/ T, where T is the time period (time taken to complete one revolution). The problem states that both cars make a complete circle in the same time 't'. Therefore, the time period T is the same for both cars. For the first car, \u03c9\u2081 = 2\u03c0 \/ t. For the second car, \u03c9\u2082 = 2\u03c0 \/ t. The ratio of their angular speeds is \u03c9\u2081 : \u03c9\u2082 = (2\u03c0 \/ t) : (2\u03c0 \/ t) = 1 : 1. The masses (m\u2081 and m\u2082) and radii (r\u2081 and r\u2082) of the cars are irrelevant for determining the ratio of angular speeds when the time period is given to be the same.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/exam.pscnotes.com\/mcq\/two-racing-cars-of-masses-m\u2081-and-m\u2082-are-moving-in-circles-of-radii-r\u2081\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ and Quiz for Exams\" \/>\n<meta property=\"article:published_time\" content=\"2025-06-01T10:17:56+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":"Two racing cars of masses m\u2081 and m\u2082 are moving in circles of radii r\u2081","description":"The correct answer is 1 : 1. Angular speed (\u03c9) is defined as the rate of change of angular displacement. For an object moving in a circle, the angular speed is given by \u03c9 = 2\u03c0 \/ T, where T is the time period (time taken to complete one revolution). The problem states that both cars make a complete circle in the same time 't'. Therefore, the time period T is the same for both cars. For the first car, \u03c9\u2081 = 2\u03c0 \/ t. For the second car, \u03c9\u2082 = 2\u03c0 \/ t. The ratio of their angular speeds is \u03c9\u2081 : \u03c9\u2082 = (2\u03c0 \/ t) : (2\u03c0 \/ t) = 1 : 1. The masses (m\u2081 and m\u2082) and radii (r\u2081 and r\u2082) of the cars are irrelevant for determining the ratio of angular speeds when the time period is given to be the same.","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\/two-racing-cars-of-masses-m\u2081-and-m\u2082-are-moving-in-circles-of-radii-r\u2081\/","og_locale":"en_US","og_type":"article","og_title":"Two racing cars of masses m\u2081 and m\u2082 are moving in circles of radii r\u2081","og_description":"The correct answer is 1 : 1. Angular speed (\u03c9) is defined as the rate of change of angular displacement. For an object moving in a circle, the angular speed is given by \u03c9 = 2\u03c0 \/ T, where T is the time period (time taken to complete one revolution). The problem states that both cars make a complete circle in the same time 't'. Therefore, the time period T is the same for both cars. For the first car, \u03c9\u2081 = 2\u03c0 \/ t. For the second car, \u03c9\u2082 = 2\u03c0 \/ t. The ratio of their angular speeds is \u03c9\u2081 : \u03c9\u2082 = (2\u03c0 \/ t) : (2\u03c0 \/ t) = 1 : 1. The masses (m\u2081 and m\u2082) and radii (r\u2081 and r\u2082) of the cars are irrelevant for determining the ratio of angular speeds when the time period is given to be the same.","og_url":"https:\/\/exam.pscnotes.com\/mcq\/two-racing-cars-of-masses-m\u2081-and-m\u2082-are-moving-in-circles-of-radii-r\u2081\/","og_site_name":"MCQ and Quiz for Exams","article_published_time":"2025-06-01T10:17:56+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\/two-racing-cars-of-masses-m%e2%82%81-and-m%e2%82%82-are-moving-in-circles-of-radii-r%e2%82%81\/","url":"https:\/\/exam.pscnotes.com\/mcq\/two-racing-cars-of-masses-m%e2%82%81-and-m%e2%82%82-are-moving-in-circles-of-radii-r%e2%82%81\/","name":"Two racing cars of masses m\u2081 and m\u2082 are moving in circles of radii r\u2081","isPartOf":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#website"},"datePublished":"2025-06-01T10:17:56+00:00","dateModified":"2025-06-01T10:17:56+00:00","author":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209"},"description":"The correct answer is 1 : 1. Angular speed (\u03c9) is defined as the rate of change of angular displacement. For an object moving in a circle, the angular speed is given by \u03c9 = 2\u03c0 \/ T, where T is the time period (time taken to complete one revolution). The problem states that both cars make a complete circle in the same time 't'. Therefore, the time period T is the same for both cars. For the first car, \u03c9\u2081 = 2\u03c0 \/ t. For the second car, \u03c9\u2082 = 2\u03c0 \/ t. The ratio of their angular speeds is \u03c9\u2081 : \u03c9\u2082 = (2\u03c0 \/ t) : (2\u03c0 \/ t) = 1 : 1. The masses (m\u2081 and m\u2082) and radii (r\u2081 and r\u2082) of the cars are irrelevant for determining the ratio of angular speeds when the time period is given to be the same.","breadcrumb":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/two-racing-cars-of-masses-m%e2%82%81-and-m%e2%82%82-are-moving-in-circles-of-radii-r%e2%82%81\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/exam.pscnotes.com\/mcq\/two-racing-cars-of-masses-m%e2%82%81-and-m%e2%82%82-are-moving-in-circles-of-radii-r%e2%82%81\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/exam.pscnotes.com\/mcq\/two-racing-cars-of-masses-m%e2%82%81-and-m%e2%82%82-are-moving-in-circles-of-radii-r%e2%82%81\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/exam.pscnotes.com\/mcq\/"},{"@type":"ListItem","position":2,"name":"UPSC CAPF","item":"https:\/\/exam.pscnotes.com\/mcq\/category\/upsc-capf\/"},{"@type":"ListItem","position":3,"name":"Two racing cars of masses m\u2081 and m\u2082 are moving in circles of radii r\u2081"}]},{"@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\/89957","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=89957"}],"version-history":[{"count":0,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts\/89957\/revisions"}],"wp:attachment":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/media?parent=89957"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/categories?post=89957"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/tags?post=89957"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}