{"id":3104,"date":"2022-05-07T06:35:20","date_gmt":"2022-05-07T06:35:20","guid":{"rendered":"https:\/\/mdr.foobrdigital.com\/?p=3104"},"modified":"2022-05-07T06:35:20","modified_gmt":"2022-05-07T06:35:20","slug":"relation-between-g-and-g","status":"publish","type":"post","link":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/2022\/05\/07\/relation-between-g-and-g\/","title":{"rendered":"Relation Between G and g"},"content":{"rendered":"\n

An object that falls under the sole influence of gravity is known as a free-falling object. A free-falling object has an acceleration of 9.8 m\/s2<\/sup>, downward (on Earth). This numerical value is so significant that it is given a special name as the acceleration of gravity. We denote it with the symbol g<\/em><\/strong>.<\/p>\n\n\n\n

The force of attraction between any two unit masses separated by a unit distance is called the universal gravitational constant. The universal gravitational constant is denoted by the symbol G<\/em><\/strong> and is measured in Nm2<\/sup>\/kg2<\/sup>. The numerical value of G is 6.67 \u00d7 10-11<\/sup> Nm\u00b2\/Kg\u00b2.<\/p>\n\n\n\n

The relation between\u00a0G<\/em><\/strong>\u00a0and\u00a0g<\/em><\/strong>\u00a0is not proportional. This means that they are independent entities.<\/p>\n\n\n\n

Relationship Between G and g<\/h2>\n\n\n\n

In physics, G and g related to each other as follows:<\/p>\n\n\n\n

g=GM\/R2<\/sup><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

Where,<\/p>\n\n\n\n

  • g is the acceleration due to the gravity<\/strong> measured in m\/s2<\/sup>.<\/li>
  • G is the universal gravitational constant<\/strong> measured in Nm2<\/sup>\/kg2<\/sup>.<\/li>
  • R is the radius<\/strong> of the massive body measured in km.<\/li>
  • M is the mass<\/strong> of the massive body measured in Kg<\/li><\/ul>\n\n\n\n

    Although there exists a formula to express the relation between g and G in physics, there is no correlation between\u00a0acceleration due to gravity\u00a0and universal gravitation constant, as the value of G is constant. The value of G is constant at any point in this universe, and G and g are not dependent on each other.<\/p>\n\n\n\n

    What is G and g?<\/h2>\n\n\n\n

    The G and g are distinct entities in physics. Below is the table of the difference between G and g.<\/p>\n\n\n\n

    <\/td>Symbol<\/strong><\/td>Definition<\/strong><\/td>Nature of Value<\/strong><\/td>Unit<\/strong><\/td><\/tr>
    Acceleration due to gravity<\/td>g<\/td>The acceleration experienced by a body under free fall due to the gravitational force of the massive body<\/td>Changes from place to place.Acceleration due to gravity of the earth is 9.8 m\/s2<\/sup><\/td>m\/s2<\/sup><\/td><\/tr>
    Universal Gravitational Constant<\/td>G<\/td>The force of attraction between two objects with unit mass separated by a unit distance at any part of this universe.<\/td>Constant at any point in this universe.G = 6.67\u00d710-11 <\/sup>Nm2<\/sup>\/kg2<\/sup><\/td>Nm2<\/sup>\/kg<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

    <\/p>\n\n\n\n

    Deriving the relationship between g and G<\/h2>\n\n\n\n

    <\/p>\n\n\n\n

    According to the\u00a0universal law of gravitation, <\/p>\n\n\n\n

    F = G M m R 2<\/sup> \u2014\u2014\u2014\u2014(1)<\/p>\n\n\n\n

    From Newton\u2019s second law of motion, we know that <\/p>\n\n\n\n

    F = m a \u2014\u2014\u2014\u2013(2)<\/p>\n\n\n\n

    If the acceleration due to gravity is g at a given point, then the above equation becomes<\/p>\n\n\n\n

    F = m g \u2014\u2014\u2014\u2013(3)<\/p>\n\n\n\n

    Substituting equation (3) in (1), we get-<\/p>\n\n\n\n

    m g = G M m R 2<\/sup><\/p>\n\n\n\n

    Simplifying the above equation, we get<\/p>\n\n\n\n

    g = G M R 2<\/sup><\/p>\n\n\n\n

    Thus, we arrive at the relationship between g and G as \u2013<\/p>\n\n\n\n

    \u21d2 g = G M R 2<\/sup><\/p>\n","protected":false},"excerpt":{"rendered":"

    An object that falls under the sole influence of gravity is known as a free-falling object. A free-falling object has an acceleration of 9.8 m\/s2, downward (on Earth). This numerical value is so significant that it is given a special name as the acceleration of gravity. We denote it with the symbol g. The force of […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[191],"tags":[],"_links":{"self":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts\/3104"}],"collection":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/comments?post=3104"}],"version-history":[{"count":0,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts\/3104\/revisions"}],"wp:attachment":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/media?parent=3104"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/categories?post=3104"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/tags?post=3104"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}