{"id":88347,"date":"2025-06-01T07:08:28","date_gmt":"2025-06-01T07:08:28","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=88347"},"modified":"2025-06-01T07:08:28","modified_gmt":"2025-06-01T07:08:28","slug":"an-object-moves-in-a-circular-path-with-a-constant-speed-which-one-of","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/an-object-moves-in-a-circular-path-with-a-constant-speed-which-one-of\/","title":{"rendered":"An object moves in a circular path with a constant speed. Which one of"},"content":{"rendered":"<p>An object moves in a circular path with a constant speed. Which one of the following statements is correct ?<\/p>\n<p>[amp_mcq option1=&#8221;The centripetal acceleration of the object is smaller for a gentle curve (i.e., curve of larger radius) than that for a sharp curve (i.e., curve of smaller radius).&#8221; option2=&#8221;The centripetal acceleration is greater for a gentle curve than that for a sharp curve.&#8221; option3=&#8221;The centripetal acceleration is the same for both, the gentle and sharp curves.&#8221; option4=&#8221;The centripetal acceleration causes the object to slow down.&#8221; correct=&#8221;option1&#8243;]<\/p>\n<div class=\"psc-box-pyq-exam-year-detail\">\n<div class=\"pyq-exam\">\n<div class=\"psc-heading\">This question was previously asked in<\/div>\n<div class=\"psc-title line-ellipsis\">UPSC NDA-2 &#8211; 2017<\/div>\n<\/div>\n<div class=\"pyq-exam-psc-buttons\"><a href=\"\/pyq\/pyq-upsc-nda-2-2017.pdf\" target=\"_blank\" class=\"psc-pdf-button\" rel=\"noopener\">Download PDF<\/a><a href=\"\/pyq-upsc-nda-2-2017\" target=\"_blank\" class=\"psc-attempt-button\" rel=\"noopener\">Attempt Online<\/a><\/div>\n<\/div>\n<section id=\"pyq-correct-answer\">\nWhen an object moves in a circular path with constant speed $v$, it experiences a centripetal acceleration $a_c$ directed towards the center of the circle. The formula for centripetal acceleration is $a_c = \\frac{v^2}{r}$, where $v$ is the speed and $r$ is the radius of the circular path. For a constant speed $v$, the centripetal acceleration is inversely proportional to the radius $r$. A gentle curve corresponds to a larger radius ($r$), while a sharp curve corresponds to a smaller radius ($r$). Therefore, for a constant speed, a larger radius (gentle curve) results in a smaller centripetal acceleration, and a smaller radius (sharp curve) results in a larger centripetal acceleration. Option A correctly states that the centripetal acceleration is smaller for a gentle curve (larger radius) than for a sharp curve (smaller radius).<br \/>\n<\/section>\n<section id=\"pyq-key-points\">\n&#8211; Centripetal acceleration $a_c = \\frac{v^2}{r}$.<br \/>\n&#8211; For constant speed $v$, $a_c \\propto \\frac{1}{r}$.<br \/>\n&#8211; Gentle curve = larger radius; Sharp curve = smaller radius.<br \/>\n<\/section>\n<section id=\"pyq-additional-information\">\nCentripetal acceleration is always perpendicular to the velocity vector in uniform circular motion and is responsible for changing the direction of velocity, thus keeping the object on the circular path, without changing its speed. Option D is incorrect because centripetal acceleration changes direction, not speed (in uniform circular motion).<br \/>\n<\/section>\n","protected":false},"excerpt":{"rendered":"<p>An object moves in a circular path with a constant speed. Which one of the following statements is correct ? [amp_mcq option1=&#8221;The centripetal acceleration of the object is smaller for a gentle curve (i.e., curve of larger radius) than that for a sharp curve (i.e., curve of smaller radius).&#8221; option2=&#8221;The centripetal acceleration is greater for &#8230; <\/p>\n<p class=\"read-more-container\"><a title=\"An object moves in a circular path with a constant speed. Which one of\" class=\"read-more button\" href=\"https:\/\/exam.pscnotes.com\/mcq\/an-object-moves-in-a-circular-path-with-a-constant-speed-which-one-of\/#more-88347\">Detailed Solution<span class=\"screen-reader-text\">An object moves in a circular path with a constant speed. Which one of<\/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":[1101,1129,1128],"class_list":["post-88347","post","type-post","status-publish","format-standard","hentry","category-upsc-nda-2","tag-1101","tag-mechanics","tag-physics","no-featured-image-padding"],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v22.2 (Yoast SEO v23.3) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>An object moves in a circular path with a constant speed. Which one of<\/title>\n<meta name=\"description\" content=\"When an object moves in a circular path with constant speed $v$, it experiences a centripetal acceleration $a_c$ directed towards the center of the circle. The formula for centripetal acceleration is $a_c = frac{v^2}{r}$, where $v$ is the speed and $r$ is the radius of the circular path. For a constant speed $v$, the centripetal acceleration is inversely proportional to the radius $r$. A gentle curve corresponds to a larger radius ($r$), while a sharp curve corresponds to a smaller radius ($r$). Therefore, for a constant speed, a larger radius (gentle curve) results in a smaller centripetal acceleration, and a smaller radius (sharp curve) results in a larger centripetal acceleration. Option A correctly states that the centripetal acceleration is smaller for a gentle curve (larger radius) than for a sharp curve (smaller radius). - Centripetal acceleration $a_c = frac{v^2}{r}$. - For constant speed $v$, $a_c propto frac{1}{r}$. - Gentle curve = larger radius; Sharp curve = smaller radius.\" \/>\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\/an-object-moves-in-a-circular-path-with-a-constant-speed-which-one-of\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"An object moves in a circular path with a constant speed. Which one of\" \/>\n<meta property=\"og:description\" content=\"When an object moves in a circular path with constant speed $v$, it experiences a centripetal acceleration $a_c$ directed towards the center of the circle. The formula for centripetal acceleration is $a_c = frac{v^2}{r}$, where $v$ is the speed and $r$ is the radius of the circular path. For a constant speed $v$, the centripetal acceleration is inversely proportional to the radius $r$. A gentle curve corresponds to a larger radius ($r$), while a sharp curve corresponds to a smaller radius ($r$). Therefore, for a constant speed, a larger radius (gentle curve) results in a smaller centripetal acceleration, and a smaller radius (sharp curve) results in a larger centripetal acceleration. Option A correctly states that the centripetal acceleration is smaller for a gentle curve (larger radius) than for a sharp curve (smaller radius). - Centripetal acceleration $a_c = frac{v^2}{r}$. - For constant speed $v$, $a_c propto frac{1}{r}$. - Gentle curve = larger radius; Sharp curve = smaller radius.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/exam.pscnotes.com\/mcq\/an-object-moves-in-a-circular-path-with-a-constant-speed-which-one-of\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ and Quiz for Exams\" \/>\n<meta property=\"article:published_time\" content=\"2025-06-01T07:08:28+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":"An object moves in a circular path with a constant speed. Which one of","description":"When an object moves in a circular path with constant speed $v$, it experiences a centripetal acceleration $a_c$ directed towards the center of the circle. The formula for centripetal acceleration is $a_c = frac{v^2}{r}$, where $v$ is the speed and $r$ is the radius of the circular path. For a constant speed $v$, the centripetal acceleration is inversely proportional to the radius $r$. A gentle curve corresponds to a larger radius ($r$), while a sharp curve corresponds to a smaller radius ($r$). Therefore, for a constant speed, a larger radius (gentle curve) results in a smaller centripetal acceleration, and a smaller radius (sharp curve) results in a larger centripetal acceleration. Option A correctly states that the centripetal acceleration is smaller for a gentle curve (larger radius) than for a sharp curve (smaller radius). - Centripetal acceleration $a_c = frac{v^2}{r}$. - For constant speed $v$, $a_c propto frac{1}{r}$. - Gentle curve = larger radius; Sharp curve = smaller radius.","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\/an-object-moves-in-a-circular-path-with-a-constant-speed-which-one-of\/","og_locale":"en_US","og_type":"article","og_title":"An object moves in a circular path with a constant speed. Which one of","og_description":"When an object moves in a circular path with constant speed $v$, it experiences a centripetal acceleration $a_c$ directed towards the center of the circle. The formula for centripetal acceleration is $a_c = frac{v^2}{r}$, where $v$ is the speed and $r$ is the radius of the circular path. For a constant speed $v$, the centripetal acceleration is inversely proportional to the radius $r$. A gentle curve corresponds to a larger radius ($r$), while a sharp curve corresponds to a smaller radius ($r$). Therefore, for a constant speed, a larger radius (gentle curve) results in a smaller centripetal acceleration, and a smaller radius (sharp curve) results in a larger centripetal acceleration. Option A correctly states that the centripetal acceleration is smaller for a gentle curve (larger radius) than for a sharp curve (smaller radius). - Centripetal acceleration $a_c = frac{v^2}{r}$. - For constant speed $v$, $a_c propto frac{1}{r}$. - Gentle curve = larger radius; Sharp curve = smaller radius.","og_url":"https:\/\/exam.pscnotes.com\/mcq\/an-object-moves-in-a-circular-path-with-a-constant-speed-which-one-of\/","og_site_name":"MCQ and Quiz for Exams","article_published_time":"2025-06-01T07:08:28+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\/an-object-moves-in-a-circular-path-with-a-constant-speed-which-one-of\/","url":"https:\/\/exam.pscnotes.com\/mcq\/an-object-moves-in-a-circular-path-with-a-constant-speed-which-one-of\/","name":"An object moves in a circular path with a constant speed. Which one of","isPartOf":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#website"},"datePublished":"2025-06-01T07:08:28+00:00","dateModified":"2025-06-01T07:08:28+00:00","author":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209"},"description":"When an object moves in a circular path with constant speed $v$, it experiences a centripetal acceleration $a_c$ directed towards the center of the circle. The formula for centripetal acceleration is $a_c = \\frac{v^2}{r}$, where $v$ is the speed and $r$ is the radius of the circular path. For a constant speed $v$, the centripetal acceleration is inversely proportional to the radius $r$. A gentle curve corresponds to a larger radius ($r$), while a sharp curve corresponds to a smaller radius ($r$). Therefore, for a constant speed, a larger radius (gentle curve) results in a smaller centripetal acceleration, and a smaller radius (sharp curve) results in a larger centripetal acceleration. Option A correctly states that the centripetal acceleration is smaller for a gentle curve (larger radius) than for a sharp curve (smaller radius). - Centripetal acceleration $a_c = \\frac{v^2}{r}$. - For constant speed $v$, $a_c \\propto \\frac{1}{r}$. - Gentle curve = larger radius; Sharp curve = smaller radius.","breadcrumb":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/an-object-moves-in-a-circular-path-with-a-constant-speed-which-one-of\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/exam.pscnotes.com\/mcq\/an-object-moves-in-a-circular-path-with-a-constant-speed-which-one-of\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/exam.pscnotes.com\/mcq\/an-object-moves-in-a-circular-path-with-a-constant-speed-which-one-of\/#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":"An object moves in a circular path with a constant speed. Which one of"}]},{"@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\/88347","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=88347"}],"version-history":[{"count":0,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts\/88347\/revisions"}],"wp:attachment":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/media?parent=88347"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/categories?post=88347"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/tags?post=88347"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}