{"id":89217,"date":"2025-06-01T09:59:12","date_gmt":"2025-06-01T09:59:12","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=89217"},"modified":"2025-06-01T09:59:12","modified_gmt":"2025-06-01T09:59:12","slug":"a-person-moves-along-a-circular-path-by-a-distance-equal-to-half-the-c","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/a-person-moves-along-a-circular-path-by-a-distance-equal-to-half-the-c\/","title":{"rendered":"A person moves along a circular path by a distance equal to half the c"},"content":{"rendered":"

A person moves along a circular path by a distance equal to half the circumference in a given time. The ratio of his average speed to his average velocity is :<\/p>\n

[amp_mcq option1=”0.5″ option2=”0.5\u03c0” option3=”0.75\u03c0” option4=”1.0″ correct=”option2″]<\/p>\n

\n
\n
This question was previously asked in<\/div>\n
UPSC CAPF – 2009<\/div>\n<\/div>\n
Download PDF<\/a>Attempt Online<\/a><\/div>\n<\/div>\n
\nThe correct option is B.
\n<\/section>\n
\nLet the circular path have radius R. The circumference is $C = 2\\pi R$.
\nThe distance covered by the person is half the circumference, $d = \\frac{1}{2} C = \\pi R$.
\nLet the time taken be $t$.
\nAverage speed is defined as the total distance traveled divided by the total time taken.
\nAverage speed = $\\frac{d}{t} = \\frac{\\pi R}{t}$.<\/p>\n

The person moves along a circular path by a distance equal to half the circumference. This means the person starts at one point on the circle and ends at the diametrically opposite point.
\nLet the starting point be A and the ending point be B, where AB is a diameter of the circle.
\nThe displacement is the shortest straight-line distance from the initial position to the final position. In this case, the displacement is the length of the diameter.
\nDisplacement = $2R$.<\/p>\n

Average velocity is defined as the total displacement divided by the total time taken.
\nAverage velocity = $\\frac{\\text{Displacement}}{t} = \\frac{2R}{t}$.<\/p>\n

The ratio of average speed to average velocity is:
\nRatio = $\\frac{\\text{Average speed}}{\\text{Average velocity}} = \\frac{\\pi R \/ t}{2R \/ t} = \\frac{\\pi R}{t} \\times \\frac{t}{2R} = \\frac{\\pi}{2}$.
\nThe value $\\frac{\\pi}{2}$ is equivalent to $0.5\\pi$.
\n<\/section>\n

\nThis question highlights the difference between speed (scalar, based on distance) and velocity (vector, based on displacement). Distance is the path length, while displacement is the change in position vector. For motion along a curved path, the distance is generally greater than the magnitude of the displacement. For a half circle, the distance is $\\pi R$ and the displacement magnitude is $2R$.
\n<\/section>\n","protected":false},"excerpt":{"rendered":"

A person moves along a circular path by a distance equal to half the circumference in a given time. The ratio of his average speed to his average velocity is : [amp_mcq option1=”0.5″ option2=”0.5\u03c0” option3=”0.75\u03c0” option4=”1.0″ correct=”option2″] This question was previously asked in UPSC CAPF – 2009 Download PDFAttempt Online The correct option is B. … <\/p>\n

Detailed SolutionA person moves along a circular path by a distance equal to half the c<\/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":[1462,1129,1128],"class_list":["post-89217","post","type-post","status-publish","format-standard","hentry","category-upsc-capf","tag-1462","tag-mechanics","tag-physics","no-featured-image-padding"],"yoast_head":"\nA person moves along a circular path by a distance equal to half the c<\/title>\n<meta name=\"description\" content=\"The correct option is B. Let the circular path have radius R. The circumference is $C = 2pi R$. The distance covered by the person is half the circumference, $d = frac{1}{2} C = pi R$. Let the time taken be $t$. Average speed is defined as the total distance traveled divided by the total time taken. Average speed = $frac{d}{t} = frac{pi R}{t}$. The person moves along a circular path by a distance equal to half the circumference. This means the person starts at one point on the circle and ends at the diametrically opposite point. Let the starting point be A and the ending point be B, where AB is a diameter of the circle. The displacement is the shortest straight-line distance from the initial position to the final position. In this case, the displacement is the length of the diameter. Displacement = $2R$. Average velocity is defined as the total displacement divided by the total time taken. Average velocity = $frac{text{Displacement}}{t} = frac{2R}{t}$. The ratio of average speed to average velocity is: Ratio = $frac{text{Average speed}}{text{Average velocity}} = frac{pi R \/ t}{2R \/ t} = frac{pi R}{t} times frac{t}{2R} = frac{pi}{2}$. The value $frac{pi}{2}$ is equivalent to $0.5pi$.\" \/>\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-person-moves-along-a-circular-path-by-a-distance-equal-to-half-the-c\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"A person moves along a circular path by a distance equal to half the c\" \/>\n<meta property=\"og:description\" content=\"The correct option is B. Let the circular path have radius R. The circumference is $C = 2pi R$. The distance covered by the person is half the circumference, $d = frac{1}{2} C = pi R$. Let the time taken be $t$. Average speed is defined as the total distance traveled divided by the total time taken. Average speed = $frac{d}{t} = frac{pi R}{t}$. The person moves along a circular path by a distance equal to half the circumference. This means the person starts at one point on the circle and ends at the diametrically opposite point. Let the starting point be A and the ending point be B, where AB is a diameter of the circle. The displacement is the shortest straight-line distance from the initial position to the final position. In this case, the displacement is the length of the diameter. Displacement = $2R$. Average velocity is defined as the total displacement divided by the total time taken. Average velocity = $frac{text{Displacement}}{t} = frac{2R}{t}$. The ratio of average speed to average velocity is: Ratio = $frac{text{Average speed}}{text{Average velocity}} = frac{pi R \/ t}{2R \/ t} = frac{pi R}{t} times frac{t}{2R} = frac{pi}{2}$. The value $frac{pi}{2}$ is equivalent to $0.5pi$.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/exam.pscnotes.com\/mcq\/a-person-moves-along-a-circular-path-by-a-distance-equal-to-half-the-c\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ and Quiz for Exams\" \/>\n<meta property=\"article:published_time\" content=\"2025-06-01T09:59:12+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 person moves along a circular path by a distance equal to half the c","description":"The correct option is B. Let the circular path have radius R. The circumference is $C = 2pi R$. The distance covered by the person is half the circumference, $d = frac{1}{2} C = pi R$. Let the time taken be $t$. Average speed is defined as the total distance traveled divided by the total time taken. Average speed = $frac{d}{t} = frac{pi R}{t}$. The person moves along a circular path by a distance equal to half the circumference. This means the person starts at one point on the circle and ends at the diametrically opposite point. Let the starting point be A and the ending point be B, where AB is a diameter of the circle. The displacement is the shortest straight-line distance from the initial position to the final position. In this case, the displacement is the length of the diameter. Displacement = $2R$. Average velocity is defined as the total displacement divided by the total time taken. Average velocity = $frac{text{Displacement}}{t} = frac{2R}{t}$. The ratio of average speed to average velocity is: Ratio = $frac{text{Average speed}}{text{Average velocity}} = frac{pi R \/ t}{2R \/ t} = frac{pi R}{t} times frac{t}{2R} = frac{pi}{2}$. The value $frac{pi}{2}$ is equivalent to $0.5pi$.","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-person-moves-along-a-circular-path-by-a-distance-equal-to-half-the-c\/","og_locale":"en_US","og_type":"article","og_title":"A person moves along a circular path by a distance equal to half the c","og_description":"The correct option is B. Let the circular path have radius R. The circumference is $C = 2pi R$. The distance covered by the person is half the circumference, $d = frac{1}{2} C = pi R$. Let the time taken be $t$. Average speed is defined as the total distance traveled divided by the total time taken. Average speed = $frac{d}{t} = frac{pi R}{t}$. The person moves along a circular path by a distance equal to half the circumference. This means the person starts at one point on the circle and ends at the diametrically opposite point. Let the starting point be A and the ending point be B, where AB is a diameter of the circle. The displacement is the shortest straight-line distance from the initial position to the final position. In this case, the displacement is the length of the diameter. Displacement = $2R$. Average velocity is defined as the total displacement divided by the total time taken. Average velocity = $frac{text{Displacement}}{t} = frac{2R}{t}$. The ratio of average speed to average velocity is: Ratio = $frac{text{Average speed}}{text{Average velocity}} = frac{pi R \/ t}{2R \/ t} = frac{pi R}{t} times frac{t}{2R} = frac{pi}{2}$. The value $frac{pi}{2}$ is equivalent to $0.5pi$.","og_url":"https:\/\/exam.pscnotes.com\/mcq\/a-person-moves-along-a-circular-path-by-a-distance-equal-to-half-the-c\/","og_site_name":"MCQ and Quiz for Exams","article_published_time":"2025-06-01T09:59:12+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-person-moves-along-a-circular-path-by-a-distance-equal-to-half-the-c\/","url":"https:\/\/exam.pscnotes.com\/mcq\/a-person-moves-along-a-circular-path-by-a-distance-equal-to-half-the-c\/","name":"A person moves along a circular path by a distance equal to half the c","isPartOf":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#website"},"datePublished":"2025-06-01T09:59:12+00:00","dateModified":"2025-06-01T09:59:12+00:00","author":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209"},"description":"The correct option is B. Let the circular path have radius R. The circumference is $C = 2\\pi R$. The distance covered by the person is half the circumference, $d = \\frac{1}{2} C = \\pi R$. Let the time taken be $t$. Average speed is defined as the total distance traveled divided by the total time taken. Average speed = $\\frac{d}{t} = \\frac{\\pi R}{t}$. The person moves along a circular path by a distance equal to half the circumference. This means the person starts at one point on the circle and ends at the diametrically opposite point. Let the starting point be A and the ending point be B, where AB is a diameter of the circle. The displacement is the shortest straight-line distance from the initial position to the final position. In this case, the displacement is the length of the diameter. Displacement = $2R$. Average velocity is defined as the total displacement divided by the total time taken. Average velocity = $\\frac{\\text{Displacement}}{t} = \\frac{2R}{t}$. The ratio of average speed to average velocity is: Ratio = $\\frac{\\text{Average speed}}{\\text{Average velocity}} = \\frac{\\pi R \/ t}{2R \/ t} = \\frac{\\pi R}{t} \\times \\frac{t}{2R} = \\frac{\\pi}{2}$. The value $\\frac{\\pi}{2}$ is equivalent to $0.5\\pi$.","breadcrumb":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/a-person-moves-along-a-circular-path-by-a-distance-equal-to-half-the-c\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/exam.pscnotes.com\/mcq\/a-person-moves-along-a-circular-path-by-a-distance-equal-to-half-the-c\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/exam.pscnotes.com\/mcq\/a-person-moves-along-a-circular-path-by-a-distance-equal-to-half-the-c\/#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":"A person moves along a circular path by a distance equal to half the c"}]},{"@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\/89217","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=89217"}],"version-history":[{"count":0,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts\/89217\/revisions"}],"wp:attachment":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/media?parent=89217"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/categories?post=89217"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/tags?post=89217"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}