{"id":29305,"date":"2025-06-20T20:56:18","date_gmt":"2025-06-20T20:56:18","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=29305"},"modified":"2025-06-20T20:56:19","modified_gmt":"2025-06-20T20:56:19","slug":"the-dimensions-of-surface-tension-are","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/the-dimensions-of-surface-tension-are\/","title":{"rendered":"The dimensions of surface tension are"},"content":{"rendered":"\n<p>The dimensions of surface tension are<\/p>\n\n\n\n<p><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\"><strong>The correct answer and explanation is:<\/strong><\/mark><\/p>\n\n\n\n<p>The dimensions of surface tension are <strong>[M T\u207b\u00b2]<\/strong> or equivalently <strong>force per unit length<\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation:<\/h3>\n\n\n\n<p>Surface tension is a physical property that represents the force acting along the surface of a liquid, causing it to behave like a stretched elastic membrane. It arises due to cohesive forces between molecules at the surface of the liquid.<\/p>\n\n\n\n<p><strong>Definition of Surface Tension:<\/strong><\/p>\n\n\n\n<p>Surface tension (usually denoted by the Greek letter \u03b3 or T) is defined as the force acting along the surface per unit length. Mathematically: Surface&nbsp;tension=ForceLength\\text{Surface tension} = \\frac{\\text{Force}}{\\text{Length}}<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Force has dimensions of mass \u00d7 acceleration, or [MLT\u22122][M L T^{-2}].<\/li>\n\n\n\n<li>Length has dimension [L][L].<\/li>\n<\/ul>\n\n\n\n<p>Therefore, the dimensions of surface tension can be written as: [MLT\u22122][L]=[MT\u22122]\\frac{[M L T^{-2}]}{[L]} = [M T^{-2}]<\/p>\n\n\n\n<p>This means surface tension has the dimensions of mass per time squared.<\/p>\n\n\n\n<p><strong>Physical Interpretation:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Surface tension is often expressed in units of Newton per meter (N\/m) in the SI system.<\/li>\n\n\n\n<li>A Newton (N) is equivalent to kg\u22c5m\/s2kg \\cdot m\/s^2, so N\/m simplifies to kg\/s2kg\/s^2, consistent with the dimensional formula above.<\/li>\n\n\n\n<li>It represents how much force is exerted along each meter of the liquid&#8217;s surface to minimize the surface area.<\/li>\n<\/ul>\n\n\n\n<p><strong>Relation to Other Quantities:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Surface tension can also be interpreted as energy per unit area. Energy has dimensions [ML2T\u22122][M L^2 T^{-2}], and area has dimensions [L2][L^2], so energy per unit area also gives [MT\u22122][M T^{-2}].<\/li>\n\n\n\n<li>This duality explains why surface tension affects phenomena such as droplet formation, capillary action, and the shape of liquid surfaces.<\/li>\n<\/ul>\n\n\n\n<p>In summary, the dimensions of surface tension are force per unit length, expressed as [MT\u22122][M T^{-2}], reflecting its role as a force acting along a line on the liquid&#8217;s surface.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The dimensions of surface tension are The correct answer and explanation is: The dimensions of surface tension are [M T\u207b\u00b2] or equivalently force per unit length. Explanation: Surface tension is a physical property that represents the force acting along the surface of a liquid, causing it to behave like a stretched elastic membrane. It arises [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-29305","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/29305","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=29305"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/29305\/revisions"}],"predecessor-version":[{"id":29306,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/29305\/revisions\/29306"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=29305"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=29305"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=29305"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}