{"id":88067,"date":"2025-06-01T07:00:49","date_gmt":"2025-06-01T07:00:49","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=88067"},"modified":"2025-06-01T07:00:49","modified_gmt":"2025-06-01T07:00:49","slug":"which-one-of-the-following-statements-regarding-a-simple-pendulum-is-c","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/which-one-of-the-following-statements-regarding-a-simple-pendulum-is-c\/","title":{"rendered":"Which one of the following statements regarding a simple pendulum is c"},"content":{"rendered":"

Which one of the following statements regarding a simple pendulum is correct? Simple pendulum has a time period independent of amplitude:<\/p>\n

[amp_mcq option1=”only for small amplitudes because then the net force on its bob is independent of its displacement.” option2=”for any amplitude because the net force on the bob is always proportional to its displacement.” option3=”for any amplitude because the net force on the bob is independent of its displacement.” option4=”only for small amplitudes because then the net force on its bob is proportional to its displacement.” correct=”option4″]<\/p>\n

\n
\n
This question was previously asked in<\/div>\n
UPSC NDA-1 – 2024<\/div>\n<\/div>\n
Download PDF<\/a>Attempt Online<\/a><\/div>\n<\/div>\n
\nThe correct statement is D. A simple pendulum has a time period independent of amplitude only for small amplitudes because then the net force on its bob is proportional to its displacement.
\n<\/section>\n
\nThe motion of a simple pendulum is approximately Simple Harmonic Motion (SHM) for small angular displacements (amplitudes). In SHM, the restoring force is directly proportional to the displacement from equilibrium (and directed towards equilibrium). For a simple pendulum, the restoring torque (or force component) is proportional to sin(theta), where theta is the angular displacement. For small theta, sin(theta) \u2248 theta (in radians), which means the restoring force is proportional to the angular displacement and, consequently, the arc displacement. This proportionality is the condition for the period to be independent of amplitude.
\n<\/section>\n
\nThe formula for the period of a simple pendulum, T = 2\u03c0 * sqrt(L\/g), is derived using the small angle approximation. For larger amplitudes, the period actually increases with amplitude because the approximation sin(theta) \u2248 theta becomes less accurate, and the motion deviates from perfect SHM.
\n<\/section>\n","protected":false},"excerpt":{"rendered":"

Which one of the following statements regarding a simple pendulum is correct? Simple pendulum has a time period independent of amplitude: [amp_mcq option1=”only for small amplitudes because then the net force on its bob is independent of its displacement.” option2=”for any amplitude because the net force on the bob is always proportional to its displacement.” … <\/p>\n

Detailed SolutionWhich one of the following statements regarding a simple pendulum is 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":[1093],"tags":[1103,1129,1128],"class_list":["post-88067","post","type-post","status-publish","format-standard","hentry","category-upsc-nda-1","tag-1103","tag-mechanics","tag-physics","no-featured-image-padding"],"yoast_head":"\nWhich one of the following statements regarding a simple pendulum is c<\/title>\n<meta name=\"description\" content=\"The correct statement is D. A simple pendulum has a time period independent of amplitude only for small amplitudes because then the net force on its bob is proportional to its displacement. The motion of a simple pendulum is approximately Simple Harmonic Motion (SHM) for small angular displacements (amplitudes). In SHM, the restoring force is directly proportional to the displacement from equilibrium (and directed towards equilibrium). For a simple pendulum, the restoring torque (or force component) is proportional to sin(theta), where theta is the angular displacement. For small theta, sin(theta) \u2248 theta (in radians), which means the restoring force is proportional to the angular displacement and, consequently, the arc displacement. This proportionality is the condition for the period to be independent of amplitude.\" \/>\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\/which-one-of-the-following-statements-regarding-a-simple-pendulum-is-c\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Which one of the following statements regarding a simple pendulum is c\" \/>\n<meta property=\"og:description\" content=\"The correct statement is D. A simple pendulum has a time period independent of amplitude only for small amplitudes because then the net force on its bob is proportional to its displacement. The motion of a simple pendulum is approximately Simple Harmonic Motion (SHM) for small angular displacements (amplitudes). In SHM, the restoring force is directly proportional to the displacement from equilibrium (and directed towards equilibrium). For a simple pendulum, the restoring torque (or force component) is proportional to sin(theta), where theta is the angular displacement. For small theta, sin(theta) \u2248 theta (in radians), which means the restoring force is proportional to the angular displacement and, consequently, the arc displacement. This proportionality is the condition for the period to be independent of amplitude.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/exam.pscnotes.com\/mcq\/which-one-of-the-following-statements-regarding-a-simple-pendulum-is-c\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ and Quiz for Exams\" \/>\n<meta property=\"article:published_time\" content=\"2025-06-01T07:00:49+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":"Which one of the following statements regarding a simple pendulum is c","description":"The correct statement is D. A simple pendulum has a time period independent of amplitude only for small amplitudes because then the net force on its bob is proportional to its displacement. The motion of a simple pendulum is approximately Simple Harmonic Motion (SHM) for small angular displacements (amplitudes). In SHM, the restoring force is directly proportional to the displacement from equilibrium (and directed towards equilibrium). For a simple pendulum, the restoring torque (or force component) is proportional to sin(theta), where theta is the angular displacement. For small theta, sin(theta) \u2248 theta (in radians), which means the restoring force is proportional to the angular displacement and, consequently, the arc displacement. This proportionality is the condition for the period to be independent of amplitude.","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\/which-one-of-the-following-statements-regarding-a-simple-pendulum-is-c\/","og_locale":"en_US","og_type":"article","og_title":"Which one of the following statements regarding a simple pendulum is c","og_description":"The correct statement is D. A simple pendulum has a time period independent of amplitude only for small amplitudes because then the net force on its bob is proportional to its displacement. The motion of a simple pendulum is approximately Simple Harmonic Motion (SHM) for small angular displacements (amplitudes). In SHM, the restoring force is directly proportional to the displacement from equilibrium (and directed towards equilibrium). For a simple pendulum, the restoring torque (or force component) is proportional to sin(theta), where theta is the angular displacement. For small theta, sin(theta) \u2248 theta (in radians), which means the restoring force is proportional to the angular displacement and, consequently, the arc displacement. This proportionality is the condition for the period to be independent of amplitude.","og_url":"https:\/\/exam.pscnotes.com\/mcq\/which-one-of-the-following-statements-regarding-a-simple-pendulum-is-c\/","og_site_name":"MCQ and Quiz for Exams","article_published_time":"2025-06-01T07:00:49+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\/which-one-of-the-following-statements-regarding-a-simple-pendulum-is-c\/","url":"https:\/\/exam.pscnotes.com\/mcq\/which-one-of-the-following-statements-regarding-a-simple-pendulum-is-c\/","name":"Which one of the following statements regarding a simple pendulum is c","isPartOf":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#website"},"datePublished":"2025-06-01T07:00:49+00:00","dateModified":"2025-06-01T07:00:49+00:00","author":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209"},"description":"The correct statement is D. A simple pendulum has a time period independent of amplitude only for small amplitudes because then the net force on its bob is proportional to its displacement. The motion of a simple pendulum is approximately Simple Harmonic Motion (SHM) for small angular displacements (amplitudes). In SHM, the restoring force is directly proportional to the displacement from equilibrium (and directed towards equilibrium). For a simple pendulum, the restoring torque (or force component) is proportional to sin(theta), where theta is the angular displacement. For small theta, sin(theta) \u2248 theta (in radians), which means the restoring force is proportional to the angular displacement and, consequently, the arc displacement. 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