{"id":186217,"date":"2025-01-24T10:32:46","date_gmt":"2025-01-24T10:32:46","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=186217"},"modified":"2025-01-24T10:32:48","modified_gmt":"2025-01-24T10:32:48","slug":"constants-and-other-possibly-useful-numbers-g-9-8m","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/01\/24\/constants-and-other-possibly-useful-numbers-g-9-8m\/","title":{"rendered":"Constants and other possibly useful numbers g = 9.8m"},"content":{"rendered":"\n<p>Constants and other possibly useful numbers g = 9.8m \/ (s ^ 2) e = 1.6 * 10 ^ &#8211; 19 * C R = k_{B}*N_{A} = 8.31 * J\/(molK) G = 6.67 * 10 ^ &#8211; 11 * (N * m ^ 2)\/(k * g ^ 2) \u0127 = h\/(2\u03c0) = 1.05 \u00d7 10-34 JS 0K = &#8211; 273 deg * C c = 3 * 10 ^ 8 * m \/ s N_{A} = 6.02 * 10 ^ 23 \/ m * ol 1atm = 1.01 * 10 ^ 5 * Pa m_{e} = 9.1 * 10 ^ &#8211; 31 * kg k_{B} = 1.38 * 10 ^ &#8211; 23 * J \/ K 1eV = 1.6 * 10 ^ &#8211; 19 * J Specific Heat (c) J\/(kg\u00b7K) kcal\/(kg\u00b0C) Aluminum 900 0.215 Constants Copper 387 0.0924 Gold 129 0.0308 Iron, steel 452 0.108 1.000 Water 4186 1. Find the ratio of the new\/old periods of a pendulum if the pendulum were transported from Earth to the Moon, where the acceleration due to gravity is 1.63m \/ (s ^ 2) .<\/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>\ue203The period TT of a simple pendulum is given by the formula:\ue204<\/p>\n\n\n\n<p>T=2\u03c0LgT = 2\\pi \\sqrt{\\frac{L}{g}}<\/p>\n\n\n\n<p>where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>TT is the period,<\/li>\n\n\n\n<li>LL is the length of the pendulum,<\/li>\n\n\n\n<li>gg is the acceleration due to gravity.\ue206<\/li>\n<\/ul>\n\n\n\n<p>\ue203This equation shows that the period is directly proportional to the square root of the pendulum&#8217;s length and inversely proportional to the square root of the acceleration due to gravity.\ue204\ue206<\/p>\n\n\n\n<p><strong>Ratio of Periods:<\/strong><\/p>\n\n\n\n<p>\ue203When a pendulum is moved from Earth to the Moon, the acceleration due to gravity changes from Earth&#8217;s gEarth=9.8\u2009m\/s2g_{\\text{Earth}} = 9.8 \\, \\text{m\/s}^2 to the Moon&#8217;s gMoon=1.63\u2009m\/s2g_{\\text{Moon}} = 1.63 \\, \\text{m\/s}^2.\ue204\ue206<\/p>\n\n\n\n<p>\ue203The ratio of the new period (TMoonT_{\\text{Moon}}) to the old period (TEarthT_{\\text{Earth}}) is:\ue204\ue206<\/p>\n\n\n\n<p>\\frac{T_{\\text{Moon}}}{T_{\\text{Earth}}} = \\sqrt{\\frac{g_{\\text{Earth}}}{g_{\\text{Moon}}}<\/p>\n\n\n\n<p>Substituting the values:<\/p>\n\n\n\n<p>TMoonTEarth=9.81.63\u22486.01\\frac{T_{\\text{Moon}}}{T_{\\text{Earth}}} = \\sqrt{\\frac{9.8}{1.63} \\approx 6.01}<\/p>\n\n\n\n<p>TMoonTEarth\u22482.45\\frac{T_{\\text{Moon}}}{T_{\\text{Earth}}} \\approx 2.45<\/p>\n\n\n\n<p>\ue203Therefore, the period of the pendulum on the Moon is approximately 2.45 times longer than on Earth.\ue204\ue206<\/p>\n\n\n\n<p><strong>Explanation:<\/strong><\/p>\n\n\n\n<p>\ue203The period of a pendulum depends on the acceleration due to gravity. On Earth, with gEarth=9.8\u2009m\/s2g_{\\text{Earth}} = 9.8 \\, \\text{m\/s}^2, the period is shorter because the gravitational pull is stronger, causing the pendulum to swing back and forth more quickly. On the Moon, with gMoon=1.63\u2009m\/s2g_{\\text{Moon}} = 1.63 \\, \\text{m\/s}^2, the weaker gravitational pull results in a longer period, as the pendulum swings more slowly.\ue204\ue206<\/p>\n\n\n\n<p>\ue203This relationship highlights how gravitational acceleration influences the motion of pendulums, and by extension, the measurement of time.\ue204\ue206<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Constants and other possibly useful numbers g = 9.8m \/ (s ^ 2) e = 1.6 * 10 ^ &#8211; 19 * C R = k_{B}*N_{A} = 8.31 * J\/(molK) G = 6.67 * 10 ^ &#8211; 11 * (N * m ^ 2)\/(k * g ^ 2) \u0127 = h\/(2\u03c0) = 1.05 \u00d7 10-34 [&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-186217","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/186217","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=186217"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/186217\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=186217"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=186217"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=186217"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}