{"id":150409,"date":"2022-03-21T18:11:39","date_gmt":"2022-03-21T12:41:39","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/?p=150409"},"modified":"2025-07-23T19:35:51","modified_gmt":"2025-07-23T14:05:51","slug":"blog-iit-jee-dimensional-formula-of-surface-tension","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/blog\/iit-jee\/dimensional-formula-of-surface-tension\/","title":{"rendered":"Dimensional Formula of Surface Tension"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_37 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" style=\"display: none;\"><label for=\"item\" aria-label=\"Table of Content\"><span style=\"display: flex;align-items: center;width: 35px;height: 30px;justify-content: center;\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/label><input type=\"checkbox\" id=\"item\"><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1' style='display:block'><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/infinitylearn.com\/surge\/blog\/iit-jee\/dimensional-formula-of-surface-tension\/#Surface_Tension_Definition\" title=\"Surface Tension Definition\">Surface Tension Definition<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/infinitylearn.com\/surge\/blog\/iit-jee\/dimensional-formula-of-surface-tension\/#Dimensional_Formula_of_Surface_Tension\" title=\"Dimensional Formula of Surface Tension\">Dimensional Formula of Surface Tension<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/infinitylearn.com\/surge\/blog\/iit-jee\/dimensional-formula-of-surface-tension\/#Explanation_of_Dimensional_Formula\" title=\"Explanation of Dimensional Formula\">Explanation of Dimensional Formula<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/infinitylearn.com\/surge\/blog\/iit-jee\/dimensional-formula-of-surface-tension\/#Units_of_Surface_Tension\" title=\"Units of Surface Tension\">Units of Surface Tension<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/infinitylearn.com\/surge\/blog\/iit-jee\/dimensional-formula-of-surface-tension\/#Conclusion\" title=\"Conclusion\">Conclusion<\/a><\/li><\/ul><\/nav><\/div>\n<p>The property of any fluid that attempts to minimize its free surface area is known as surface tension. The Force per length acting on an imaginary line drawn tangentially on the free surface of a liquid is used to calculate its surface tension. <span style=\"color: #0000ff;\"><strong>Surface tension<\/strong><\/span> S = Force\/Length, equal to F\/l, equal to work done\/area change. The SI unit is Nm<sup>-1<\/sup> or Jm<sup>-2<\/sup>, and the dimensional formula of surface tension is [MT<sup>-2<\/sup>]. The quantity is a scalar value. Surface tension is a molecular phenomenon that is electrical and is the root cause of Force. The surface tension of a liquid is determined solely by its composition and is unaffected by the film surface or line length. Because of the surface tension properties of the liquid, small drops are spherical. The concept of <a href=\"https:\/\/infinitylearn.com\/surge\/blog\/iit-jee\/dimensions-of-tension\/\" target=\"_blank\" rel=\"noopener\"><span style=\"color: #0000ff;\"><strong>Surface tension and its dimension<\/strong><\/span><\/a> is an important topic for <strong><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/infinitylearn.com\/jee\" target=\"_blank\" rel=\"noopener\">JEE Preparation<\/a><\/span><\/strong>.<\/p>\n<p style=\"text-align: center;\"><em><strong>J<a href=\"https:\/\/infinitylearn.com\/surge\/iit-jee\/jee-advanced-result\/\" target=\"_blank\" rel=\"noopener\">EE Advanced Result 2024<\/a><\/strong><\/em><\/p>\n<p><strong>Surface Tension<\/strong> is a physical property of liquids that describes the force acting on the surface of a liquid, which causes it to behave like a stretched elastic sheet. This property is due to the attractive forces between the molecules at the surface of the liquid. Surface tension is responsible for phenomena such as water droplets forming spherical shapes and insects walking on water.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Surface_Tension_Definition\"><\/span>Surface Tension Definition<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Surface tension can be defined as the force per unit length acting along the surface of a liquid. It is represented by the symbol <strong>\u03b3<\/strong> (gamma) and is measured in terms of force per unit length, usually in newtons per meter (N\/m).<\/p>\n<p>Mathematically, surface tension is expressed as:<\/p>\n<div class=\"formula\">\n<p><strong>Surface Tension (\u03b3)<\/strong> = <strong>Force (F)<\/strong> \/ <strong>Length (L)<\/strong><\/p>\n<\/div>\n<h2><span class=\"ez-toc-section\" id=\"Dimensional_Formula_of_Surface_Tension\"><\/span>Dimensional Formula of Surface Tension<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The dimensional formula is an expression that shows how and in what combination the fundamental quantities (mass, length, time, etc.) contribute to a given physical quantity.<\/p>\n<p>To find the dimensional formula of surface tension, we need to express it in terms of its fundamental quantities.<\/p>\n<p>Since surface tension is the ratio of force to length, we start with the dimensional formula for force. According to Newton&#8217;s second law, <strong>Force (F)<\/strong> is given by:<\/p>\n<div class=\"formula\">\n<p>F = ma<\/p>\n<\/div>\n<p>Where:<\/p>\n<ul>\n<li><strong>m<\/strong> = mass<\/li>\n<li><strong>a<\/strong> = acceleration<\/li>\n<\/ul>\n<p>The dimensional formula of force is derived as:<\/p>\n<div class=\"formula\">\n<p><strong>Dimensional Formula of Force (F)<\/strong> = [M L T<sup>-2<\/sup>]\n<\/div>\n<p>Now, surface tension is force per unit length:<\/p>\n<div class=\"formula\">\n<p><strong>Surface Tension<\/strong> = Force (F) \/ Length (L)<\/p>\n<\/div>\n<p>So, the dimensional formula of surface tension is:<\/p>\n<div class=\"formula\">\n<p><strong>Dimensional Formula of Surface Tension (\u03b3)<\/strong> = [M L T<sup>-2<\/sup>] \/ [L] = [M T<sup>-2<\/sup>]\n<\/div>\n<p>Thus, the <strong>dimensional formula of surface tension<\/strong> is:<\/p>\n<div class=\"formula\">\n<p><strong>[M T<sup>-2<\/sup>]<\/strong><\/p>\n<\/div>\n<h2><span class=\"ez-toc-section\" id=\"Explanation_of_Dimensional_Formula\"><\/span>Explanation of Dimensional Formula<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<ul>\n<li><strong>M<\/strong> represents mass.<\/li>\n<li><strong>L<\/strong> represents length.<\/li>\n<li><strong>T<\/strong> represents time.<\/li>\n<\/ul>\n<p>In the dimensional formula [M T<sup>-2<\/sup>], there is no length (L) term because it gets canceled out when force is divided by length. The formula indicates that surface tension depends on mass and time but not directly on length.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Units_of_Surface_Tension\"><\/span>Units of Surface Tension<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The SI unit of surface tension is <strong>newtons per meter (N\/m)<\/strong>. It can also be expressed in terms of energy per unit area, such as <strong>joules per square meter (J\/m\u00b2)<\/strong>, since 1 N\/m is equivalent to 1 J\/m\u00b2.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Conclusion\"><\/span>Conclusion<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Surface tension plays an important role in everyday phenomena, especially involving liquids. Understanding its dimensional formula <strong>[M T<sup>-2<\/sup>]<\/strong> helps us grasp how surface tension is related to other physical quantities like mass and time.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The property of any fluid that attempts to minimize its free surface area is known as surface tension. The Force [&hellip;]<\/p>\n","protected":false},"author":7,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"Dimensional Formula of Surface Tension","_yoast_wpseo_title":"How to Derive the Dimensional Formula of Surface Tension","_yoast_wpseo_metadesc":"The property of any fluid that attempts to minimize its free surface area is known as surface tension. Surface Tension Dimensional Formula.","custom_permalink":"blog\/iit-jee\/dimensional-formula-of-surface-tension\/"},"categories":[53,57],"tags":[],"table_tags":[],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v17.9 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>How to Derive the Dimensional Formula of Surface Tension<\/title>\n<meta name=\"description\" content=\"The property of any fluid that attempts to minimize its free surface area is known as surface tension. Surface Tension Dimensional Formula.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/infinitylearn.com\/surge\/blog\/iit-jee\/dimensional-formula-of-surface-tension\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"How to Derive the Dimensional Formula of Surface Tension\" \/>\n<meta property=\"og:description\" content=\"The property of any fluid that attempts to minimize its free surface area is known as surface tension. Surface Tension Dimensional Formula.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/infinitylearn.com\/surge\/blog\/iit-jee\/dimensional-formula-of-surface-tension\/\" \/>\n<meta property=\"og:site_name\" content=\"Infinity Learn by Sri Chaitanya\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/InfinityLearn.SriChaitanya\/\" \/>\n<meta property=\"article:published_time\" content=\"2022-03-21T12:41:39+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2025-07-23T14:05:51+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2025\/04\/infinitylearn.jpg\" \/>\n\t<meta property=\"og:image:width\" content=\"1920\" \/>\n\t<meta property=\"og:image:height\" content=\"1008\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/jpeg\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:creator\" content=\"@InfinityLearn_\" \/>\n<meta name=\"twitter:site\" content=\"@InfinityLearn_\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"Prasad Gupta\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"3 minutes\" \/>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"How to Derive the Dimensional Formula of Surface Tension","description":"The property of any fluid that attempts to minimize its free surface area is known as surface tension. Surface Tension Dimensional Formula.","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:\/\/infinitylearn.com\/surge\/blog\/iit-jee\/dimensional-formula-of-surface-tension\/","og_locale":"en_US","og_type":"article","og_title":"How to Derive the Dimensional Formula of Surface Tension","og_description":"The property of any fluid that attempts to minimize its free surface area is known as surface tension. Surface Tension Dimensional Formula.","og_url":"https:\/\/infinitylearn.com\/surge\/blog\/iit-jee\/dimensional-formula-of-surface-tension\/","og_site_name":"Infinity Learn by Sri Chaitanya","article_publisher":"https:\/\/www.facebook.com\/InfinityLearn.SriChaitanya\/","article_published_time":"2022-03-21T12:41:39+00:00","article_modified_time":"2025-07-23T14:05:51+00:00","og_image":[{"width":1920,"height":1008,"url":"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2025\/04\/infinitylearn.jpg","type":"image\/jpeg"}],"twitter_card":"summary_large_image","twitter_creator":"@InfinityLearn_","twitter_site":"@InfinityLearn_","twitter_misc":{"Written by":"Prasad Gupta","Est. reading time":"3 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Organization","@id":"https:\/\/infinitylearn.com\/surge\/#organization","name":"Infinity Learn","url":"https:\/\/infinitylearn.com\/surge\/","sameAs":["https:\/\/www.facebook.com\/InfinityLearn.SriChaitanya\/","https:\/\/www.instagram.com\/infinitylearn_by_srichaitanya\/","https:\/\/www.linkedin.com\/company\/infinity-learn-by-sri-chaitanya\/","https:\/\/www.youtube.com\/c\/InfinityLearnEdu","https:\/\/twitter.com\/InfinityLearn_"],"logo":{"@type":"ImageObject","@id":"https:\/\/infinitylearn.com\/surge\/#logo","inLanguage":"en-US","url":"","contentUrl":"","caption":"Infinity Learn"},"image":{"@id":"https:\/\/infinitylearn.com\/surge\/#logo"}},{"@type":"WebSite","@id":"https:\/\/infinitylearn.com\/surge\/#website","url":"https:\/\/infinitylearn.com\/surge\/","name":"Infinity Learn by Sri Chaitanya","description":"Surge","publisher":{"@id":"https:\/\/infinitylearn.com\/surge\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/infinitylearn.com\/surge\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"en-US"},{"@type":"WebPage","@id":"https:\/\/infinitylearn.com\/surge\/blog\/iit-jee\/dimensional-formula-of-surface-tension\/#webpage","url":"https:\/\/infinitylearn.com\/surge\/blog\/iit-jee\/dimensional-formula-of-surface-tension\/","name":"How to Derive the Dimensional Formula of Surface Tension","isPartOf":{"@id":"https:\/\/infinitylearn.com\/surge\/#website"},"datePublished":"2022-03-21T12:41:39+00:00","dateModified":"2025-07-23T14:05:51+00:00","description":"The property of any fluid that attempts to minimize its free surface area is known as surface tension. Surface Tension Dimensional Formula.","breadcrumb":{"@id":"https:\/\/infinitylearn.com\/surge\/blog\/iit-jee\/dimensional-formula-of-surface-tension\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/infinitylearn.com\/surge\/blog\/iit-jee\/dimensional-formula-of-surface-tension\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/infinitylearn.com\/surge\/blog\/iit-jee\/dimensional-formula-of-surface-tension\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/infinitylearn.com\/surge\/"},{"@type":"ListItem","position":2,"name":"Dimensional Formula of Surface Tension"}]},{"@type":"Article","@id":"https:\/\/infinitylearn.com\/surge\/blog\/iit-jee\/dimensional-formula-of-surface-tension\/#article","isPartOf":{"@id":"https:\/\/infinitylearn.com\/surge\/blog\/iit-jee\/dimensional-formula-of-surface-tension\/#webpage"},"author":{"@id":"https:\/\/infinitylearn.com\/surge\/#\/schema\/person\/143c89c9c2f5e56ed91f96dde47b0b05"},"headline":"Dimensional Formula of Surface Tension","datePublished":"2022-03-21T12:41:39+00:00","dateModified":"2025-07-23T14:05:51+00:00","mainEntityOfPage":{"@id":"https:\/\/infinitylearn.com\/surge\/blog\/iit-jee\/dimensional-formula-of-surface-tension\/#webpage"},"wordCount":550,"publisher":{"@id":"https:\/\/infinitylearn.com\/surge\/#organization"},"articleSection":["Blog","IIT-JEE"],"inLanguage":"en-US"},{"@type":"Person","@id":"https:\/\/infinitylearn.com\/surge\/#\/schema\/person\/143c89c9c2f5e56ed91f96dde47b0b05","name":"Prasad Gupta","image":{"@type":"ImageObject","@id":"https:\/\/infinitylearn.com\/surge\/#personlogo","inLanguage":"en-US","url":"https:\/\/secure.gravatar.com\/avatar\/200104b443e586c76c46cadc113d931c?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/200104b443e586c76c46cadc113d931c?s=96&d=mm&r=g","caption":"Prasad Gupta"},"url":"https:\/\/infinitylearn.com\/surge\/author\/prasad\/"}]}},"_links":{"self":[{"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/posts\/150409"}],"collection":[{"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/users\/7"}],"replies":[{"embeddable":true,"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/comments?post=150409"}],"version-history":[{"count":1,"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/posts\/150409\/revisions"}],"predecessor-version":[{"id":771253,"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/posts\/150409\/revisions\/771253"}],"wp:attachment":[{"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/media?parent=150409"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/categories?post=150409"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/tags?post=150409"},{"taxonomy":"table_tags","embeddable":true,"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/table_tags?post=150409"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}