{"id":90212,"date":"2025-06-01T10:23:07","date_gmt":"2025-06-01T10:23:07","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=90212"},"modified":"2025-06-01T10:23:07","modified_gmt":"2025-06-01T10:23:07","slug":"if-the-amplitude-of-oscillation-of-a-simple-pendulum-is-very-small-th","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/if-the-amplitude-of-oscillation-of-a-simple-pendulum-is-very-small-th\/","title":{"rendered":"If the amplitude of oscillation of a simple pendulum is very small, th"},"content":{"rendered":"<p>If the amplitude of oscillation of a simple pendulum is very small, then its time period of oscillation<\/p>\n<ul>\n<li>1. depends on the length of the pendulum, L<\/li>\n<li>2. depends on the acceleration due to gravity, g<\/li>\n<li>3. depends upon the mass of the bob of the pendulum, m<\/li>\n<li>4. does not depend upon the amplitude of the pendulum, A<\/li>\n<\/ul>\n<p>Select the correct answer using the code given below.<\/p>\n<p>[amp_mcq option1=&#8221;1, 2 and 3&#8243; option2=&#8221;1, 2 and 4&#8243; option3=&#8221;2, 3 and 4&#8243; option4=&#8221;1 and 4 only&#8221; correct=&#8221;option2&#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 CAPF &#8211; 2018<\/div>\n<\/div>\n<div class=\"pyq-exam-psc-buttons\"><a href=\"\/pyq\/pyq-upsc-capf-2018.pdf\" target=\"_blank\" class=\"psc-pdf-button\" rel=\"noopener\">Download PDF<\/a><a href=\"\/pyq-upsc-capf-2018\" target=\"_blank\" class=\"psc-attempt-button\" rel=\"noopener\">Attempt Online<\/a><\/div>\n<\/div>\n<section id=\"pyq-correct-answer\">\nThe time period of oscillation of a simple pendulum, when the amplitude is very small, depends on the length of the pendulum and the acceleration due to gravity, but not on the mass of the bob or the amplitude.<br \/>\n<\/section>\n<section id=\"pyq-key-points\">\nFor small oscillations (amplitude A is very small), the formula for the time period (T) of a simple pendulum is given by T = 2\u03c0\u221a(L\/g), where L is the length of the pendulum and g is the acceleration due to gravity. This formula explicitly shows that the time period depends on L and g, but it does not contain the mass (m) of the bob or the amplitude (A). The condition of small amplitude is crucial for this simplified formula to hold, implying independence from amplitude in this specific case.<br \/>\n<\/section>\n<section id=\"pyq-additional-information\">\nFor larger amplitudes, the time period of a simple pendulum is slightly longer and does depend on the amplitude. However, the question specifically states &#8220;amplitude&#8230; is very small&#8221;, which validates the use of the small-angle approximation formula.<br \/>\n<\/section>\n","protected":false},"excerpt":{"rendered":"<p>If the amplitude of oscillation of a simple pendulum is very small, then its time period of oscillation 1. depends on the length of the pendulum, L 2. depends on the acceleration due to gravity, g 3. depends upon the mass of the bob of the pendulum, m 4. does not depend upon the amplitude &#8230; <\/p>\n<p class=\"read-more-container\"><a title=\"If the amplitude of oscillation of a simple pendulum is very small, th\" class=\"read-more button\" href=\"https:\/\/exam.pscnotes.com\/mcq\/if-the-amplitude-of-oscillation-of-a-simple-pendulum-is-very-small-th\/#more-90212\">Detailed Solution<span class=\"screen-reader-text\">If the amplitude of oscillation of a simple pendulum is very small, th<\/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":[1114,1129,1128],"class_list":["post-90212","post","type-post","status-publish","format-standard","hentry","category-upsc-capf","tag-1114","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>If the amplitude of oscillation of a simple pendulum is very small, th<\/title>\n<meta name=\"description\" content=\"The time period of oscillation of a simple pendulum, when the amplitude is very small, depends on the length of the pendulum and the acceleration due to gravity, but not on the mass of the bob or the amplitude. For small oscillations (amplitude A is very small), the formula for the time period (T) of a simple pendulum is given by T = 2\u03c0\u221a(L\/g), where L is the length of the pendulum and g is the acceleration due to gravity. This formula explicitly shows that the time period depends on L and g, but it does not contain the mass (m) of the bob or the amplitude (A). The condition of small amplitude is crucial for this simplified formula to hold, implying independence from amplitude in this specific case.\" \/>\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\/if-the-amplitude-of-oscillation-of-a-simple-pendulum-is-very-small-th\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"If the amplitude of oscillation of a simple pendulum is very small, th\" \/>\n<meta property=\"og:description\" content=\"The time period of oscillation of a simple pendulum, when the amplitude is very small, depends on the length of the pendulum and the acceleration due to gravity, but not on the mass of the bob or the amplitude. For small oscillations (amplitude A is very small), the formula for the time period (T) of a simple pendulum is given by T = 2\u03c0\u221a(L\/g), where L is the length of the pendulum and g is the acceleration due to gravity. This formula explicitly shows that the time period depends on L and g, but it does not contain the mass (m) of the bob or the amplitude (A). The condition of small amplitude is crucial for this simplified formula to hold, implying independence from amplitude in this specific case.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/exam.pscnotes.com\/mcq\/if-the-amplitude-of-oscillation-of-a-simple-pendulum-is-very-small-th\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ and Quiz for Exams\" \/>\n<meta property=\"article:published_time\" content=\"2025-06-01T10:23:07+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":"If the amplitude of oscillation of a simple pendulum is very small, th","description":"The time period of oscillation of a simple pendulum, when the amplitude is very small, depends on the length of the pendulum and the acceleration due to gravity, but not on the mass of the bob or the amplitude. For small oscillations (amplitude A is very small), the formula for the time period (T) of a simple pendulum is given by T = 2\u03c0\u221a(L\/g), where L is the length of the pendulum and g is the acceleration due to gravity. This formula explicitly shows that the time period depends on L and g, but it does not contain the mass (m) of the bob or the amplitude (A). The condition of small amplitude is crucial for this simplified formula to hold, implying independence from amplitude in this specific case.","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\/if-the-amplitude-of-oscillation-of-a-simple-pendulum-is-very-small-th\/","og_locale":"en_US","og_type":"article","og_title":"If the amplitude of oscillation of a simple pendulum is very small, th","og_description":"The time period of oscillation of a simple pendulum, when the amplitude is very small, depends on the length of the pendulum and the acceleration due to gravity, but not on the mass of the bob or the amplitude. For small oscillations (amplitude A is very small), the formula for the time period (T) of a simple pendulum is given by T = 2\u03c0\u221a(L\/g), where L is the length of the pendulum and g is the acceleration due to gravity. This formula explicitly shows that the time period depends on L and g, but it does not contain the mass (m) of the bob or the amplitude (A). The condition of small amplitude is crucial for this simplified formula to hold, implying independence from amplitude in this specific case.","og_url":"https:\/\/exam.pscnotes.com\/mcq\/if-the-amplitude-of-oscillation-of-a-simple-pendulum-is-very-small-th\/","og_site_name":"MCQ and Quiz for Exams","article_published_time":"2025-06-01T10:23:07+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\/if-the-amplitude-of-oscillation-of-a-simple-pendulum-is-very-small-th\/","url":"https:\/\/exam.pscnotes.com\/mcq\/if-the-amplitude-of-oscillation-of-a-simple-pendulum-is-very-small-th\/","name":"If the amplitude of oscillation of a simple pendulum is very small, th","isPartOf":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#website"},"datePublished":"2025-06-01T10:23:07+00:00","dateModified":"2025-06-01T10:23:07+00:00","author":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209"},"description":"The time period of oscillation of a simple pendulum, when the amplitude is very small, depends on the length of the pendulum and the acceleration due to gravity, but not on the mass of the bob or the amplitude. For small oscillations (amplitude A is very small), the formula for the time period (T) of a simple pendulum is given by T = 2\u03c0\u221a(L\/g), where L is the length of the pendulum and g is the acceleration due to gravity. This formula explicitly shows that the time period depends on L and g, but it does not contain the mass (m) of the bob or the amplitude (A). The condition of small amplitude is crucial for this simplified formula to hold, implying independence from amplitude in this specific case.","breadcrumb":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/if-the-amplitude-of-oscillation-of-a-simple-pendulum-is-very-small-th\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/exam.pscnotes.com\/mcq\/if-the-amplitude-of-oscillation-of-a-simple-pendulum-is-very-small-th\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/exam.pscnotes.com\/mcq\/if-the-amplitude-of-oscillation-of-a-simple-pendulum-is-very-small-th\/#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":"If the amplitude of oscillation of a simple pendulum is very small, th"}]},{"@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\/90212","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=90212"}],"version-history":[{"count":0,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts\/90212\/revisions"}],"wp:attachment":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/media?parent=90212"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/categories?post=90212"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/tags?post=90212"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}