{"id":85590,"date":"2025-06-01T03:22:11","date_gmt":"2025-06-01T03:22:11","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=85590"},"modified":"2025-06-01T03:22:11","modified_gmt":"2025-06-01T03:22:11","slug":"which-one-of-the-following-physical-quantities-has-the-same-dimensions","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/which-one-of-the-following-physical-quantities-has-the-same-dimensions\/","title":{"rendered":"Which one of the following physical quantities has the same dimensions"},"content":{"rendered":"

Which one of the following physical quantities has the same dimensions as that of Planck’s constant h?<\/p>\n

[amp_mcq option1=”Linear momentum” option2=”Angular momentum” option3=”Force” option4=”Potential energy” correct=”option2″]<\/p>\n

\n
\n
This question was previously asked in<\/div>\n
UPSC CDS-2 – 2016<\/div>\n<\/div>\n
Download PDF<\/a>Attempt Online<\/a><\/div>\n<\/div>\n
\nThe physical quantity that has the same dimensions as Planck’s constant (h) is angular momentum.
\n<\/section>\n
\n– Planck’s constant (h) relates the energy (E) of a photon to its frequency (\u03bd) by the equation E = h\u03bd. The dimensions of E are [ML\u00b2T\u207b\u00b2] and the dimensions of \u03bd are [T\u207b\u00b9]. Therefore, the dimensions of h are [E\/\u03bd] = [ML\u00b2T\u207b\u00b2] \/ [T\u207b\u00b9] = [ML\u00b2T\u207b\u00b9].
\n– Let’s check the dimensions of the given options:
\n – Linear momentum (p = mv): [M] * [LT\u207b\u00b9] = [MLT\u207b\u00b9].
\n – Angular momentum (L = I\u03c9 or L = rp): [Moment of inertia * Angular velocity] or [Radius * Linear momentum]. Dimensions are [ML\u00b2] * [T\u207b\u00b9] or [L] * [MLT\u207b\u00b9] = [ML\u00b2T\u207b\u00b9].
\n – Force (F = ma): [M] * [LT\u207b\u00b2] = [MLT\u207b\u00b2].
\n – Potential energy (e.g., mgh): [M] * [LT\u207b\u00b2] * [L] = [ML\u00b2T\u207b\u00b2].
\n– Comparing the dimensions, angular momentum [ML\u00b2T\u207b\u00b9] has the same dimensions as Planck’s constant [ML\u00b2T\u207b\u00b9].
\n<\/section>\n
\nIn quantum mechanics, angular momentum is quantized in units of Planck’s reduced constant (\u0127 = h\/2\u03c0), which has the same dimensions as h. This dimensional equivalence is not a coincidence but reflects a fundamental connection between energy, frequency, and angular momentum in quantum physics.
\n<\/section>\n","protected":false},"excerpt":{"rendered":"

Which one of the following physical quantities has the same dimensions as that of Planck’s constant h? [amp_mcq option1=”Linear momentum” option2=”Angular momentum” option3=”Force” option4=”Potential energy” correct=”option2″] This question was previously asked in UPSC CDS-2 – 2016 Download PDFAttempt Online The physical quantity that has the same dimensions as Planck’s constant (h) is angular momentum. – … <\/p>\n

Detailed SolutionWhich one of the following physical quantities has the same dimensions<\/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":[1088],"tags":[1098,1140,1128],"class_list":["post-85590","post","type-post","status-publish","format-standard","hentry","category-upsc-cds-2","tag-1098","tag-measurement-unit","tag-physics","no-featured-image-padding"],"yoast_head":"\nWhich one of the following physical quantities has the same dimensions<\/title>\n<meta name=\"description\" content=\"The physical quantity that has the same dimensions as Planck's constant (h) is angular momentum. - Planck's constant (h) relates the energy (E) of a photon to its frequency (\u03bd) by the equation E = h\u03bd. The dimensions of E are [ML\u00b2T\u207b\u00b2] and the dimensions of \u03bd are [T\u207b\u00b9]. Therefore, the dimensions of h are [E\/\u03bd] = [ML\u00b2T\u207b\u00b2] \/ [T\u207b\u00b9] = [ML\u00b2T\u207b\u00b9]. - Let's check the dimensions of the given options: - Linear momentum (p = mv): [M] * [LT\u207b\u00b9] = [MLT\u207b\u00b9]. - Angular momentum (L = I\u03c9 or L = rp): [Moment of inertia * Angular velocity] or [Radius * Linear momentum]. Dimensions are [ML\u00b2] * [T\u207b\u00b9] or [L] * [MLT\u207b\u00b9] = [ML\u00b2T\u207b\u00b9]. - Force (F = ma): [M] * [LT\u207b\u00b2] = [MLT\u207b\u00b2]. - Potential energy (e.g., mgh): [M] * [LT\u207b\u00b2] * [L] = [ML\u00b2T\u207b\u00b2]. - Comparing the dimensions, angular momentum [ML\u00b2T\u207b\u00b9] has the same dimensions as Planck's constant [ML\u00b2T\u207b\u00b9].\" \/>\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-physical-quantities-has-the-same-dimensions\/\" \/>\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 physical quantities has the same dimensions\" \/>\n<meta property=\"og:description\" content=\"The physical quantity that has the same dimensions as Planck's constant (h) is angular momentum. - Planck's constant (h) relates the energy (E) of a photon to its frequency (\u03bd) by the equation E = h\u03bd. The dimensions of E are [ML\u00b2T\u207b\u00b2] and the dimensions of \u03bd are [T\u207b\u00b9]. Therefore, the dimensions of h are [E\/\u03bd] = [ML\u00b2T\u207b\u00b2] \/ [T\u207b\u00b9] = [ML\u00b2T\u207b\u00b9]. - Let's check the dimensions of the given options: - Linear momentum (p = mv): [M] * [LT\u207b\u00b9] = [MLT\u207b\u00b9]. - Angular momentum (L = I\u03c9 or L = rp): [Moment of inertia * Angular velocity] or [Radius * Linear momentum]. Dimensions are [ML\u00b2] * [T\u207b\u00b9] or [L] * [MLT\u207b\u00b9] = [ML\u00b2T\u207b\u00b9]. - Force (F = ma): [M] * [LT\u207b\u00b2] = [MLT\u207b\u00b2]. - Potential energy (e.g., mgh): [M] * [LT\u207b\u00b2] * [L] = [ML\u00b2T\u207b\u00b2]. - Comparing the dimensions, angular momentum [ML\u00b2T\u207b\u00b9] has the same dimensions as Planck's constant [ML\u00b2T\u207b\u00b9].\" \/>\n<meta property=\"og:url\" content=\"https:\/\/exam.pscnotes.com\/mcq\/which-one-of-the-following-physical-quantities-has-the-same-dimensions\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ and Quiz for Exams\" \/>\n<meta property=\"article:published_time\" content=\"2025-06-01T03:22:11+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 physical quantities has the same dimensions","description":"The physical quantity that has the same dimensions as Planck's constant (h) is angular momentum. - Planck's constant (h) relates the energy (E) of a photon to its frequency (\u03bd) by the equation E = h\u03bd. The dimensions of E are [ML\u00b2T\u207b\u00b2] and the dimensions of \u03bd are [T\u207b\u00b9]. Therefore, the dimensions of h are [E\/\u03bd] = [ML\u00b2T\u207b\u00b2] \/ [T\u207b\u00b9] = [ML\u00b2T\u207b\u00b9]. - Let's check the dimensions of the given options: - Linear momentum (p = mv): [M] * [LT\u207b\u00b9] = [MLT\u207b\u00b9]. - Angular momentum (L = I\u03c9 or L = rp): [Moment of inertia * Angular velocity] or [Radius * Linear momentum]. Dimensions are [ML\u00b2] * [T\u207b\u00b9] or [L] * [MLT\u207b\u00b9] = [ML\u00b2T\u207b\u00b9]. - Force (F = ma): [M] * [LT\u207b\u00b2] = [MLT\u207b\u00b2]. - Potential energy (e.g., mgh): [M] * [LT\u207b\u00b2] * [L] = [ML\u00b2T\u207b\u00b2]. - Comparing the dimensions, angular momentum [ML\u00b2T\u207b\u00b9] has the same dimensions as Planck's constant [ML\u00b2T\u207b\u00b9].","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-physical-quantities-has-the-same-dimensions\/","og_locale":"en_US","og_type":"article","og_title":"Which one of the following physical quantities has the same dimensions","og_description":"The physical quantity that has the same dimensions as Planck's constant (h) is angular momentum. - Planck's constant (h) relates the energy (E) of a photon to its frequency (\u03bd) by the equation E = h\u03bd. The dimensions of E are [ML\u00b2T\u207b\u00b2] and the dimensions of \u03bd are [T\u207b\u00b9]. Therefore, the dimensions of h are [E\/\u03bd] = [ML\u00b2T\u207b\u00b2] \/ [T\u207b\u00b9] = [ML\u00b2T\u207b\u00b9]. - Let's check the dimensions of the given options: - Linear momentum (p = mv): [M] * [LT\u207b\u00b9] = [MLT\u207b\u00b9]. - Angular momentum (L = I\u03c9 or L = rp): [Moment of inertia * Angular velocity] or [Radius * Linear momentum]. Dimensions are [ML\u00b2] * [T\u207b\u00b9] or [L] * [MLT\u207b\u00b9] = [ML\u00b2T\u207b\u00b9]. - Force (F = ma): [M] * [LT\u207b\u00b2] = [MLT\u207b\u00b2]. - Potential energy (e.g., mgh): [M] * [LT\u207b\u00b2] * [L] = [ML\u00b2T\u207b\u00b2]. - Comparing the dimensions, angular momentum [ML\u00b2T\u207b\u00b9] has the same dimensions as Planck's constant [ML\u00b2T\u207b\u00b9].","og_url":"https:\/\/exam.pscnotes.com\/mcq\/which-one-of-the-following-physical-quantities-has-the-same-dimensions\/","og_site_name":"MCQ and Quiz for Exams","article_published_time":"2025-06-01T03:22:11+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-physical-quantities-has-the-same-dimensions\/","url":"https:\/\/exam.pscnotes.com\/mcq\/which-one-of-the-following-physical-quantities-has-the-same-dimensions\/","name":"Which one of the following physical quantities has the same dimensions","isPartOf":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#website"},"datePublished":"2025-06-01T03:22:11+00:00","dateModified":"2025-06-01T03:22:11+00:00","author":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209"},"description":"The physical quantity that has the same dimensions as Planck's constant (h) is angular momentum. - Planck's constant (h) relates the energy (E) of a photon to its frequency (\u03bd) by the equation E = h\u03bd. The dimensions of E are [ML\u00b2T\u207b\u00b2] and the dimensions of \u03bd are [T\u207b\u00b9]. Therefore, the dimensions of h are [E\/\u03bd] = [ML\u00b2T\u207b\u00b2] \/ [T\u207b\u00b9] = [ML\u00b2T\u207b\u00b9]. - Let's check the dimensions of the given options: - Linear momentum (p = mv): [M] * [LT\u207b\u00b9] = [MLT\u207b\u00b9]. - Angular momentum (L = I\u03c9 or L = rp): [Moment of inertia * Angular velocity] or [Radius * Linear momentum]. Dimensions are [ML\u00b2] * [T\u207b\u00b9] or [L] * [MLT\u207b\u00b9] = [ML\u00b2T\u207b\u00b9]. - Force (F = ma): [M] * [LT\u207b\u00b2] = [MLT\u207b\u00b2]. - Potential energy (e.g., mgh): [M] * [LT\u207b\u00b2] * [L] = [ML\u00b2T\u207b\u00b2]. - Comparing the dimensions, angular momentum [ML\u00b2T\u207b\u00b9] has the same dimensions as Planck's constant [ML\u00b2T\u207b\u00b9].","breadcrumb":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/which-one-of-the-following-physical-quantities-has-the-same-dimensions\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/exam.pscnotes.com\/mcq\/which-one-of-the-following-physical-quantities-has-the-same-dimensions\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/exam.pscnotes.com\/mcq\/which-one-of-the-following-physical-quantities-has-the-same-dimensions\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/exam.pscnotes.com\/mcq\/"},{"@type":"ListItem","position":2,"name":"UPSC CDS-2","item":"https:\/\/exam.pscnotes.com\/mcq\/category\/upsc-cds-2\/"},{"@type":"ListItem","position":3,"name":"Which one of the following physical quantities has the same dimensions"}]},{"@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\/85590","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=85590"}],"version-history":[{"count":0,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts\/85590\/revisions"}],"wp:attachment":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/media?parent=85590"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/categories?post=85590"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/tags?post=85590"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}