{"id":63386,"date":"2023-12-14T13:00:47","date_gmt":"2023-12-14T07:30:47","guid":{"rendered":"https:\/\/pwonlyias.com\/stage\/?post_type=ncert-notes&#038;p=63386"},"modified":"2024-09-26T12:24:11","modified_gmt":"2024-09-26T06:54:11","slug":"universal-law-of-gravitation","status":"publish","type":"ncert-notes","link":"https:\/\/pwonlyias.com\/stage\/ncert-notes\/universal-law-of-gravitation","title":{"rendered":"Universal Law of Gravitation: Significance, Value, &#038; Celestial Forces"},"content":{"rendered":"<p><span style=\"font-size: 24pt;\"><b>Newton&#8217;s Universal Law and Its Cosmic Significance<\/b><\/span><\/p>\n<p><span style=\"font-weight: 400;\">The Universal Law of Gravitation, formulated by <\/span><b>Sir Isaac Newton, i<\/b><span style=\"font-weight: 400;\">s pivotal in understanding the fundamental forces governing the cosmos. This law not only elucidates <\/span><b>planetary orbits <\/b><span style=\"font-weight: 400;\">but also enables advancements in<\/span><b> astronomy, space exploration,<\/b><span style=\"font-weight: 400;\"> and a profound comprehension of the universe&#8217;s intricate mechanics.<\/span><\/p>\n<p><span style=\"font-size: 18pt;\"><b>Gravity&#8217;s Influence and the Cosmic Dance and Earthly Mysteries<\/b><\/span><\/p>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><b>Help in Understanding Universe: <\/b><span style=\"font-weight: 400;\">The Universal Law of Gravitation is foundational in understanding the <\/span><b>large-scale structure<\/b><span style=\"font-weight: 400;\"> and behaviour of the universe, from why apples fall from trees to the intricate dances of galaxies.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><b>Crucial Law: <\/b><span style=\"font-weight: 400;\">The Universal Law of Gravitation is crucial because it unifies the understanding of several phenomena.\u00a0<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Few of the more common ones are listed as under:<\/span>\n<ul>\n<li><b>Earthly Attraction<\/b><span style=\"font-weight: 400;\">: It explains why things fall towards the Earth.<\/span><\/li>\n<li><b>Moon&#8217;s Orbit<\/b><span style=\"font-weight: 400;\">: The motion of the moon around the Earth is due to the gravitational attraction between them.<\/span><\/li>\n<li><b>Planetary Motion<\/b><span style=\"font-weight: 400;\">: Planets orbit the Sun due to gravitational forces.<\/span><\/li>\n<li><b>Tidal Phenomena<\/b><span style=\"font-weight: 400;\">: Tides in the oceans are significantly influenced by the gravitational forces exerted by the Moon and, to a lesser extent, the Sun.<\/span><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<h2><span style=\"font-size: 18pt;\"><b>Free Fall and Gravity: Forces That Shape our Descent<\/b><\/span><\/h2>\n<ul>\n<li><span style=\"font-weight: 400;\">Objects are said to be in free fall when they are only influenced by the gravitational force of the Earth, with no other forces (like air resistance) acting on them.<\/span><\/li>\n<li><b>Acceleration due to Gravity (g): <\/b><span style=\"font-weight: 400;\">Objects in free fall experience an acceleration towards the Earth due to its gravitational pull. This acceleration is denoted as <\/span><b>g (unit: m s<\/b><b>-2<\/b><b>)<\/b><span style=\"font-weight: 400;\"> and is termed as the <\/span><b>&#8220;acceleration due to gravity&#8221;.\u00a0<\/b><\/li>\n<li><b>Gravitational Force on a Falling Object:<\/b><span style=\"font-weight: 400;\">\u00a0<\/span><\/li>\n<\/ul>\n<p style=\"padding-left: 80px;\"><span style=\"font-weight: 400;\">F=mg\u00a0<\/span><\/p>\n<p style=\"padding-left: 80px;\"><span style=\"font-weight: 400;\">Where:\u00a0<\/span><\/p>\n<p style=\"padding-left: 80px;\"><span style=\"font-weight: 400;\">m = mass of the object;\u00a0<\/span><\/p>\n<p style=\"padding-left: 80px;\"><span style=\"font-weight: 400;\">g = acceleration due to gravity<\/span><\/p>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><b>Relation with Universal Gravitational Constant:<\/b><span style=\"font-weight: 400;\">\u00a0<\/span><\/li>\n<\/ul>\n<p style=\"padding-left: 80px;\"><span style=\"font-weight: 400;\">mg = G (M \u00d7 m \/ d<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\"> ) or,<\/span><\/p>\n<p style=\"padding-left: 80px;\"><span style=\"font-weight: 400;\">\u00a0\u00a0\u00a0g = G (M \/ d<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\"> ),\u00a0<\/span><\/p>\n<p style=\"padding-left: 80px;\"><span style=\"font-weight: 400;\">where:\u00a0<\/span><\/p>\n<p style=\"padding-left: 80px;\"><span style=\"font-weight: 400;\">G = Universal gravitational constant,\u00a0<\/span><\/p>\n<p style=\"padding-left: 80px;\"><span style=\"font-weight: 400;\">M = Mass of the Earth,\u00a0<\/span><\/p>\n<p style=\"padding-left: 80px;\"><span style=\"font-weight: 400;\">R = Radius of the Earth<\/span><\/p>\n<ul>\n<li aria-level=\"1\"><b>Variation with Latitude: <\/b><span style=\"font-weight: 400;\">Earth is not a perfect sphere; it&#8217;s slightly flattened at the poles and bulges at the equator. Thus, g is slightly greater at the poles than at the equator.<\/span><\/li>\n<\/ul>\n<h2><span style=\"font-size: 18pt;\"><b>Calculating the Value of g:<\/b><\/span><\/h2>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Using Known Values:\u00a0<\/span><\/li>\n<\/ul>\n<p style=\"padding-left: 40px;\"><span style=\"font-weight: 400;\">g = G (M \/ R<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\">)\u00a0<\/span><\/p>\n<p style=\"padding-left: 40px;\"><span style=\"font-weight: 400;\">Using values:\u00a0<\/span><\/p>\n<p style=\"padding-left: 40px;\"><span style=\"font-weight: 400;\">g = 6.7\u00d710<\/span><span style=\"font-weight: 400;\">\u221211 <\/span><span style=\"font-weight: 400;\">Nm<\/span><span style=\"font-weight: 400;\">2 <\/span><span style=\"font-weight: 400;\">\/ kg<\/span><span style=\"font-weight: 400;\">-2<\/span><span style=\"font-weight: 400;\"> \u00d7 6\u00d710<\/span><span style=\"font-weight: 400;\">24<\/span><span style=\"font-weight: 400;\">kg \/ (6.4 \u00d7 10<\/span><span style=\"font-weight: 400;\">6<\/span><span style=\"font-weight: 400;\"> m)<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\"> .\u00a0<\/span><\/p>\n<p style=\"padding-left: 40px;\"><span style=\"font-weight: 400;\">After calculation, we get\u00a0<\/span><\/p>\n<p style=\"padding-left: 40px;\"><span style=\"font-weight: 400;\">g =9.8 ms<\/span><span style=\"font-weight: 400;\">-2<\/span><\/p>\n<p style=\"padding-left: 40px;\"><span style=\"font-weight: 400;\">Hence, the standard value for the acceleration due to gravity on the surface of Earth is\u00a0<\/span><\/p>\n<p style=\"padding-left: 40px;\"><b>g = 9.8 ms<\/b><b>-2<\/b><\/p>\n<h2><span style=\"font-size: 18pt;\"><b>Free Fall and Acceleration: Uncovering the\u00a0 Universal Law Gravitational of Gravitational Motion<\/b><\/span><\/h2>\n<ul>\n<li><b>Galileo&#8217;s Experiment:<\/b>\n<ul>\n<li><span style=\"font-weight: 400;\">Galileo, in an experiment from the Leaning Tower of Pisa, demonstrated that all objects, irrespective of their mass, fall at the same rate in the absence of air resistance.<\/span><\/li>\n<\/ul>\n<\/li>\n<li><b>Equations of Motion in Free Fall:<\/b>\n<ul>\n<li><span style=\"font-weight: 400;\">With <\/span><b>g<\/b><span style=\"font-weight: 400;\"> as constant near Earth&#8217;s surface, equations of uniformly accelerated motion apply. Here, acceleration a is replaced by g:<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"3\"><span style=\"font-weight: 400;\">v= u+gt<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"3\"><span style=\"font-weight: 400;\">s = ut + \u00bd\u00a0 \u200bgt<\/span><span style=\"font-weight: 400;\">2<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"3\"><span style=\"font-weight: 400;\">v<\/span><span style=\"font-weight: 400;\">2 <\/span><span style=\"font-weight: 400;\">= u<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\"> + 2gs\u00a0<\/span><\/li>\n<\/ul>\n<\/li>\n<li><span style=\"font-weight: 400;\">Here: u = Initial velocity, v = Final velocity, s = Distance covered in time t<\/span><\/li>\n<li><span style=\"font-weight: 400;\">The direction of g is taken positive when it&#8217;s in the direction of motion (downwards) and negative when opposing it (like in case of an object thrown upwards).<\/span><\/li>\n<\/ul>\n<table style=\"width: 98.6882%;\">\n<tbody>\n<tr>\n<th style=\"width: 100%; border-style: solid; border-color: #000000; background-color: #e9ebe8; vertical-align: middle;\">\n<p style=\"text-align: left;\"><span style=\"color: #000000;\"><b>Example:<\/b><span style=\"font-weight: 400;\"> A car falls off a ledge and drops to the ground in 0.5 s. Let g = 10 m s<\/span><span style=\"font-weight: 400;\">\u20132<\/span><span style=\"font-weight: 400;\"> (for simplifying the calculations).\u00a0<\/span><\/span><\/p>\n<p style=\"text-align: left;\"><span style=\"font-weight: 400; color: #000000;\">(i) \u00a0 What is its speed on striking the ground?<\/span><\/p>\n<p style=\"text-align: left;\"><span style=\"font-weight: 400; color: #000000;\">(ii)\u00a0 What is its average speed during the 0.5 s?<\/span><\/p>\n<p style=\"text-align: left;\"><span style=\"font-weight: 400; color: #000000;\">(iii) How high is the ledge from the ground?<\/span><\/p>\n<p style=\"text-align: left;\"><span style=\"color: #000000;\"><b>Solution:\u00a0<\/b><\/span><\/p>\n<p style=\"text-align: left;\"><span style=\"color: #000000;\"><span style=\"font-weight: 400;\">Time, t = 1\u20442 second<\/span><span style=\"font-weight: 400;\"><br \/>\n<\/span><span style=\"font-weight: 400;\">Initial velocity, u = 0\u00a0 m s<\/span><span style=\"font-weight: 400;\">\u20131<\/span><span style=\"font-weight: 400;\"><br \/>\n<\/span><span style=\"font-weight: 400;\">Acceleration due to gravity, g = 10 m s<\/span><span style=\"font-weight: 400;\">\u20132<\/span><span style=\"font-weight: 400;\">\u00a0<\/span><\/span><\/p>\n<p style=\"text-align: left;\"><span style=\"color: #000000;\"><span style=\"font-weight: 400;\">Acceleration of the car, a = + 10 m s<\/span><span style=\"font-weight: 400;\">\u20132<\/span><span style=\"font-weight: 400;\">\u00a0 (downward)\u00a0<\/span><\/span><\/p>\n<p style=\"text-align: left;\"><span style=\"color: #000000;\"><span style=\"font-weight: 400;\">(i) speed v = a t<\/span><span style=\"font-weight: 400;\"><br \/>\n<\/span><span style=\"font-weight: 400;\">v = 10ms<\/span><span style=\"font-weight: 400;\">\u20132<\/span><span style=\"font-weight: 400;\">\u00a0 \u00d7 0.5s\u00a0<\/span><\/span><\/p>\n<p style=\"text-align: left;\"><span style=\"color: #000000;\"><span style=\"font-weight: 400;\">= 5ms<\/span><span style=\"font-weight: 400;\">\u20131<\/span><span style=\"font-weight: 400;\">\u00a0<\/span><\/span><\/p>\n<p style=\"text-align: left;\"><span style=\"font-weight: 400; color: #000000;\">(ii) average speed = u + v \/ 2\u00a0<\/span><\/p>\n<p style=\"text-align: left;\"><span style=\"color: #000000;\"><span style=\"font-weight: 400;\">= (0ms<\/span><span style=\"font-weight: 400;\">\u20131 <\/span><span style=\"font-weight: 400;\">+ 5ms<\/span><span style=\"font-weight: 400;\">\u20131<\/span><span style=\"font-weight: 400;\">) \/ 2\u00a0<\/span><\/span><\/p>\n<p style=\"text-align: left;\"><span style=\"color: #000000;\"><span style=\"font-weight: 400;\">= 2.5 m s<\/span><span style=\"font-weight: 400;\">\u20131<\/span><span style=\"font-weight: 400;\"><br \/>\n<\/span><span style=\"font-weight: 400;\">(iii) distance travelled, s = 1\u20442 a t<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\">\u00a0<\/span><\/span><\/p>\n<p style=\"text-align: left;\"><span style=\"color: #000000;\"><span style=\"font-weight: 400;\">= 1\u20442 \u00d7 10ms<\/span><span style=\"font-weight: 400;\">\u20132<\/span><span style=\"font-weight: 400;\"> \u00d7 (0.5s)<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\"> = 1\u20442 \u00d7 10ms<\/span><span style=\"font-weight: 400;\">\u20132<\/span><span style=\"font-weight: 400;\"> \u00d7 0.25 s<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\"> = 1.25 m\u00a0<\/span><\/span><\/p>\n<p style=\"text-align: left;\"><span style=\"font-weight: 400; color: #000000;\">Thus,\u00a0<\/span><\/p>\n<p style=\"text-align: left;\"><span style=\"color: #000000;\"><span style=\"font-weight: 400;\">(i) its speed on striking the ground = 5 m s<\/span><span style=\"font-weight: 400;\">\u20131<\/span><span style=\"font-weight: 400;\">\u00a0<\/span><\/span><\/p>\n<p style=\"text-align: left;\"><span style=\"color: #000000;\"><span style=\"font-weight: 400;\">(ii) its average speed during the 0.5 s = 2.5 m s<\/span><span style=\"font-weight: 400;\">\u20131<\/span><span style=\"font-weight: 400;\">\u00a0<\/span><\/span><\/p>\n<p style=\"text-align: left;\"><span style=\"font-weight: 400; color: #000000;\">(iii) height of the ledge from the ground = 1.25 m.\u00a0<\/span><\/p>\n<\/th>\n<\/tr>\n<\/tbody>\n<\/table>\n","protected":false},"featured_media":0,"parent":0,"template":"","notes-subjects":[4568],"subject-chapters":[4704],"acf":[],"_links":{"self":[{"href":"https:\/\/pwonlyias.com\/stage\/wp-json\/wp\/v2\/ncert-notes\/63386"}],"collection":[{"href":"https:\/\/pwonlyias.com\/stage\/wp-json\/wp\/v2\/ncert-notes"}],"about":[{"href":"https:\/\/pwonlyias.com\/stage\/wp-json\/wp\/v2\/types\/ncert-notes"}],"wp:attachment":[{"href":"https:\/\/pwonlyias.com\/stage\/wp-json\/wp\/v2\/media?parent=63386"}],"wp:term":[{"taxonomy":"notes-subjects","embeddable":true,"href":"https:\/\/pwonlyias.com\/stage\/wp-json\/wp\/v2\/notes-subjects?post=63386"},{"taxonomy":"subject-chapters","embeddable":true,"href":"https:\/\/pwonlyias.com\/stage\/wp-json\/wp\/v2\/subject-chapters?post=63386"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}