{"id":151273,"date":"2024-10-09T19:12:14","date_gmt":"2024-10-09T19:12:14","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=151273"},"modified":"2024-10-09T19:12:17","modified_gmt":"2024-10-09T19:12:17","slug":"the-si-unit-of-force-the-kilogram-meter-per-second-squared-kg-%c2%b7-m-s2","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/10\/09\/the-si-unit-of-force-the-kilogram-meter-per-second-squared-kg-%c2%b7-m-s2\/","title":{"rendered":"The SI unit of force, the kilogram-meter per second squared (kg \u00b7 m\/s2)"},"content":{"rendered":"\n<p>The SI unit of force, the kilogram-meter per second squared (kg \u00b7 m\/s2), is called the newton (N). Find the dimensions and the SI units of the constant G in Newton&#8217;s law of gravitation F = Gm1m2\/r2. (For the dimension use L for length, M for mass, and T for time. For the units use m for meters, kg for kilograms, and s for seconds.)<\/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>To find the dimensions and SI units of the gravitational constant ( G ) in Newton&#8217;s law of gravitation, we start with 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 (in newtons, ( N )),<\/li>\n\n\n\n<li>( m_1 ) and ( m_2 ) are the masses of the two objects (in kilograms, ( kg )),<\/li>\n\n\n\n<li>( r ) is the distance between the centers of the two masses (in meters, ( m )),<\/li>\n\n\n\n<li>( G ) is the gravitational constant.<\/li>\n<\/ul>\n\n\n\n<p><strong>Step 1: Identify the units and dimensions of each component.<\/strong><\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Force (( F ))<\/strong>: The SI unit of force is the newton (N), which can be expressed in terms of base SI units:<br>[<br>1 \\, N = 1 \\, kg \\cdot m\/s^2<br>]<br>Thus, the dimensions of force are:<br>[<br>[F] = [M][L][T^{-2}]<br>]<\/li>\n\n\n\n<li><strong>Mass (( m_1 ) and ( m_2 ))<\/strong>: The unit of mass is kilograms (( kg )):<br>[<br>[m] = [M]<br>]<\/li>\n\n\n\n<li><strong>Distance (( r ))<\/strong>: The unit of distance is meters (( m )):<br>[<br>[r] = [L]<br>]<\/li>\n<\/ol>\n\n\n\n<p><strong>Step 2: Substitute into the equation to solve for ( G ).<\/strong><\/p>\n\n\n\n<p>Rearranging the equation for ( G ):<br>[<br>G = \\frac{F r^2}{m_1 m_2}<br>]<\/p>\n\n\n\n<p><strong>Step 3: Substitute the dimensions and units into this expression.<\/strong><\/p>\n\n\n\n<p>Using the units and dimensions we identified:<br>[<br>[G] = \\frac{[M][L][T^{-2}] \\cdot [L^2]}{[M]^2}<br>]<br>This simplifies to:<br>[<br>[G] = \\frac{[M][L^3][T^{-2}]}{[M^2]} = [M^{-1}][L^3][T^{-2}]<br>]<\/p>\n\n\n\n<p><strong>Step 4: Find the SI units of ( G ).<\/strong><\/p>\n\n\n\n<p>Substituting the base units:<br>[<br>[G] = \\frac{m^3}{kg \\cdot s^2}<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Conclusion<\/h3>\n\n\n\n<p>The dimensions of the gravitational constant ( G ) are:<br>[<br>[G] = [M^{-1}][L^3][T^{-2}]<br>]<\/p>\n\n\n\n<p>The SI units of ( G ) are:<br>[<br>[G] = \\frac{m^3}{kg \\cdot s^2}<br>]<\/p>\n\n\n\n<p>This shows how ( G ) relates the gravitational force to the masses and the distance between them, playing a critical role in our understanding of gravitation in physics. The dimensions of ( G ) reflect its role in measuring how mass and distance influence gravitational attraction, encapsulating fundamental properties of gravity in the universe.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The SI unit of force, the kilogram-meter per second squared (kg \u00b7 m\/s2), is called the newton (N). Find the dimensions and the SI units of the constant G in Newton&#8217;s law of gravitation F = Gm1m2\/r2. (For the dimension use L for length, M for mass, and T for time. For the units use [&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-151273","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/151273","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=151273"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/151273\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=151273"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=151273"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=151273"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}