{"id":191616,"date":"2025-02-15T09:15:45","date_gmt":"2025-02-15T09:15:45","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=191616"},"modified":"2025-02-15T09:15:47","modified_gmt":"2025-02-15T09:15:47","slug":"newtons-law-of-universal-gravitation-is-f-gmm2-r%c2%b2","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/02\/15\/newtons-law-of-universal-gravitation-is-f-gmm2-r%c2%b2\/","title":{"rendered":"Newton&#8217;s law of universal gravitation is F Gmm2\/r\u00b2"},"content":{"rendered":"\n<p>Newton&#8217;s law of universal gravitation is F Gmm2\/r\u00b2, where F is the magnitude of the gravitational force exerted by one object on another, m\u2081 and m\u2082 are the masses of the ob-jects, and r is the distance between them. Determine the dimensions and the SI units of the proportionality constant G.<\/p>\n\n\n\n<p><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\"><strong>The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n<p>Newton&#8217;s law of universal gravitation is given by the equation:<\/p>\n\n\n\n<p>[<br>F = G \\frac{m_1 m_2}{r^2}<br>]<\/p>\n\n\n\n<p>Where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>( F ) is the gravitational force between two objects (measured in Newtons, N),<\/li>\n\n\n\n<li>( G ) is the gravitational constant (the quantity we want to determine),<\/li>\n\n\n\n<li>( m_1 ) and ( m_2 ) are the masses of the two objects (measured in kilograms, kg),<\/li>\n\n\n\n<li>( r ) is the distance between the centers of the two masses (measured in meters, m).<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Dimensions of Gravitational Force<\/h3>\n\n\n\n<p>The gravitational force ( F ) is measured in Newtons, and the dimensional formula of force (from Newton&#8217;s second law, ( F = ma )) is:<\/p>\n\n\n\n<p>[<br>[F] = M L T^{-2}<br>]<\/p>\n\n\n\n<p>Where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>( M ) represents mass,<\/li>\n\n\n\n<li>( L ) represents length,<\/li>\n\n\n\n<li>( T ) represents time.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Dimensions of the Other Quantities<\/h3>\n\n\n\n<p>The dimensional formulas for ( m_1 ), ( m_2 ), and ( r ) are:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>( [m_1] = [m_2] = M ),<\/li>\n\n\n\n<li>( [r] = L ).<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Step 3: Rearranging the Equation<\/h3>\n\n\n\n<p>Now, substitute the dimensional formulas into Newton&#8217;s law of universal gravitation:<\/p>\n\n\n\n<p>[<br>[F] = [G] \\frac{[m_1][m_2]}{[r]^2}<br>]<\/p>\n\n\n\n<p>Substituting the known dimensional formulas:<\/p>\n\n\n\n<p>[<br>M L T^{-2} = [G] \\frac{M^2}{L^2}<br>]<\/p>\n\n\n\n<p>Solving for the dimensions of ( G ):<\/p>\n\n\n\n<p>[<br>[G] = \\frac{M L^3 T^{-2}}{M^2} = M^{-1} L^3 T^{-2}<br>]<\/p>\n\n\n\n<p>Thus, the dimensions of the gravitational constant ( G ) are ( [G] = M^{-1} L^3 T^{-2} ).<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 4: SI Units of ( G )<\/h3>\n\n\n\n<p>To find the SI units of ( G ), we use the fact that:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>( M ) is measured in kilograms (kg),<\/li>\n\n\n\n<li>( L ) is measured in meters (m),<\/li>\n\n\n\n<li>( T ) is measured in seconds (s).<\/li>\n<\/ul>\n\n\n\n<p>Therefore, the SI units of ( G ) are:<\/p>\n\n\n\n<p>[<br>\\text{SI units of } G = \\frac{\\text{kg}^{-1} \\text{m}^3}{\\text{s}^2}<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answer:<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The dimensions of ( G ) are ( M^{-1} L^3 T^{-2} ).<\/li>\n\n\n\n<li>The SI units of ( G ) are ( \\text{kg}^{-1} \\text{m}^3 \\text{s}^{-2} ).<\/li>\n<\/ul>\n\n\n\n<p>I will now generate an image to visualize the equation and the dimensions.<\/p>\n\n\n\n<p>Here is an educational diagram illustrating Newton&#8217;s Law of Universal Gravitation, including the dimensions and SI units of the gravitational constant ( G ). Let me know if you&#8217;d like any adjustments or further explanation!<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/02\/image-605.png\" alt=\"\" class=\"wp-image-191617\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Newton&#8217;s law of universal gravitation is F Gmm2\/r\u00b2, where F is the magnitude of the gravitational force exerted by one object on another, m\u2081 and m\u2082 are the masses of the ob-jects, and r is the distance between them. Determine the dimensions and the SI units of the proportionality constant G. The Correct Answer and [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-191616","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/191616","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=191616"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/191616\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=191616"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=191616"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=191616"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}