{"id":264358,"date":"2022-09-10T13:12:41","date_gmt":"2022-09-10T07:42:41","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/question\/at-a-point-above-the-surface-of-the-earth-the-gravitational-potential-is-%e2%88%925-12x107jkg%e2%88%921-and-the-acceleration-due-to-gravity-is-6-4-ms%e2%88%922-assuming\/"},"modified":"2022-09-10T13:12:41","modified_gmt":"2022-09-10T07:42:41","slug":"at-a-point-above-the-surface-of-the-earth-the-gravitational-potential-is-%e2%88%925-12x107jkg%e2%88%921-and-the-acceleration-due-to-gravity-is-6-4-ms%e2%88%922-assuming","status":"publish","type":"questions","link":"https:\/\/infinitylearn.com\/surge\/question\/physics\/at-a-point-above-the-surface-of-the-earth-the-gravitational\/","title":{"rendered":"At a point above the surface of the earth, the gravitational potential is\u00a0\u22125.12\u00d7107Jkg\u22121\u00a0and the acceleration due to gravity is\u00a06.4\u00a0ms\u22122.\u00a0Assuming the mean radius of the earth to be\u00a06400 km, the height of this point above the earth’s surface is."},"content":{"rendered":"","protected":false},"author":1,"template":"","meta":{"_yoast_wpseo_focuskw":"","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"At a point above the surface of the earth, the gravitational potential is\u00a0\u22125.12\u00d7107Jkg\u22121\u00a0and the acceleration due to gravity is\u00a06.4\u00a0ms\u22122.\u00a0Assuming the mean radius of the earth to be\u00a06400 km, the height of this point above the earth's surface is.","custom_permalink":"question\/physics\/at-a-point-above-the-surface-of-the-earth-the-gravitational\/"},"categories":[],"acf":{"question":"

At a point above the surface of the earth, the gravitational potential is \u2212<\/mo>5.12<\/mn>\u00d7<\/mo>10<\/mn>7<\/mn><\/msup>J<\/mi>kg<\/mi>\u2212<\/mo>1<\/mn><\/mrow><\/msup><\/math> and the acceleration due to gravity is 6.4<\/mn> <\/mo>ms<\/mi>\u2212<\/mo>2<\/mn><\/mrow><\/msup>. <\/mtext><\/math>Assuming the mean radius of the earth to be 6400 km, the height of this point above the earth's surface is.<\/p>","options":[{"option":"

1400 km<\/p>","correct":false},{"option":"

1500 km<\/p>","correct":false},{"option":"

1600 km<\/p>","correct":true},{"option":"

1700 km<\/p>","correct":false}],"solution":"

Let  r<\/mtext><\/math> be the distance of the given point from the centre of the earth. Then Gravitational potential<\/p>

=<\/mo>\u2212<\/mo>GM<\/mi>r<\/mi><\/mfrac>=<\/mo>\u2212<\/mo>5<\/mn>.12<\/mo>\u00d7<\/mo>10<\/mn>7<\/mn><\/msup>\u2026<\/mo>(<\/mo>i<\/mi>)<\/mo><\/math><\/p>

And acceleration due to gravity,<\/p>

g<\/mi>=<\/mo>GM<\/mi>r<\/mi>2<\/mn><\/msup><\/mfrac>=<\/mo>6<\/mn>.4<\/mo>\u2026<\/mo>(<\/mo>ii<\/mi>)<\/mo><\/math><\/p>

Dividing Eq. (i) by Eq. (ii), we get<\/p>

r<\/mi>=<\/mo>5.12<\/mn>\u00d7<\/mo>10<\/mn>7<\/mn><\/msup><\/mrow>6.4<\/mn><\/mfrac><\/math><\/p>

=<\/mo>8<\/mn>\u00d7<\/mo>10<\/mn>6<\/mn><\/msup>m<\/mi><\/math><\/p>

= 8000 km<\/p>

\u2234<\/mo><\/math>  Height of the point from earth's surface =<\/mo>r<\/mi>\u2212<\/mo>R<\/mi>=<\/mo>8000<\/mn>\u2212<\/mo>6400<\/mn><\/math> = 1600 km<\/p>","subject":""},"yoast_head":"\nAt a point above the surface of the earth, the gravitational potential is\u00a0\u22125.12\u00d7107Jkg\u22121\u00a0and the acceleration due to gravity is\u00a06.4\u00a0ms\u22122.\u00a0Assuming the mean radius of the earth to be\u00a06400 km, the height of this point above the earth's surface is. - Infinity Learn by Sri Chaitanya<\/title>\n<meta name=\"description\" content=\"At a point above the surface of the earth, the gravitational potential is\u00a0\u22125.12\u00d7107Jkg\u22121\u00a0and the acceleration due to gravity is\u00a06.4\u00a0ms\u22122.\u00a0Assuming the mean radius of the earth to be\u00a06400 km, the height of this point above the earth's surface is.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/infinitylearn.com\/surge\/question\/physics\/at-a-point-above-the-surface-of-the-earth-the-gravitational\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"At a point above the surface of the earth, the gravitational potential is\u00a0\u22125.12\u00d7107Jkg\u22121\u00a0and the acceleration due to gravity is\u00a06.4\u00a0ms\u22122.\u00a0Assuming the mean radius of the earth to be\u00a06400 km, the height of this point above the earth's surface is. - Infinity Learn by Sri Chaitanya\" \/>\n<meta property=\"og:description\" content=\"At a point above the surface of the earth, the gravitational potential is\u00a0\u22125.12\u00d7107Jkg\u22121\u00a0and the acceleration due to gravity is\u00a06.4\u00a0ms\u22122.\u00a0Assuming the mean radius of the earth to be\u00a06400 km, the height of this point above the earth's surface is.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/infinitylearn.com\/surge\/question\/physics\/at-a-point-above-the-surface-of-the-earth-the-gravitational\/\" \/>\n<meta property=\"og:site_name\" content=\"Infinity Learn by Sri Chaitanya\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/InfinityLearn.SriChaitanya\/\" \/>\n<meta property=\"og:image\" content=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2025\/04\/infinitylearn.jpg\" \/>\n\t<meta property=\"og:image:width\" content=\"1920\" \/>\n\t<meta property=\"og:image:height\" content=\"1008\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/jpeg\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:site\" content=\"@InfinityLearn_\" \/>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"At a point above the surface of the earth, the gravitational potential is\u00a0\u22125.12\u00d7107Jkg\u22121\u00a0and the acceleration due to gravity is\u00a06.4\u00a0ms\u22122.\u00a0Assuming the mean radius of the earth to be\u00a06400 km, the height of this point above the earth's surface is. - Infinity Learn by Sri Chaitanya","description":"At a point above the surface of the earth, the gravitational potential is\u00a0\u22125.12\u00d7107Jkg\u22121\u00a0and the acceleration due to gravity is\u00a06.4\u00a0ms\u22122.\u00a0Assuming the mean radius of the earth to be\u00a06400 km, the height of this point above the earth's surface is.","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/infinitylearn.com\/surge\/question\/physics\/at-a-point-above-the-surface-of-the-earth-the-gravitational\/","og_locale":"en_US","og_type":"article","og_title":"At a point above the surface of the earth, the gravitational potential is\u00a0\u22125.12\u00d7107Jkg\u22121\u00a0and the acceleration due to gravity is\u00a06.4\u00a0ms\u22122.\u00a0Assuming the mean radius of the earth to be\u00a06400 km, the height of this point above the earth's surface is. - Infinity Learn by Sri Chaitanya","og_description":"At a point above the surface of the earth, the gravitational potential is\u00a0\u22125.12\u00d7107Jkg\u22121\u00a0and the acceleration due to gravity is\u00a06.4\u00a0ms\u22122.\u00a0Assuming the mean radius of the earth to be\u00a06400 km, the height of this point above the earth's surface is.","og_url":"https:\/\/infinitylearn.com\/surge\/question\/physics\/at-a-point-above-the-surface-of-the-earth-the-gravitational\/","og_site_name":"Infinity Learn by Sri Chaitanya","article_publisher":"https:\/\/www.facebook.com\/InfinityLearn.SriChaitanya\/","og_image":[{"width":1920,"height":1008,"url":"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2025\/04\/infinitylearn.jpg","type":"image\/jpeg"}],"twitter_card":"summary_large_image","twitter_site":"@InfinityLearn_","schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Organization","@id":"https:\/\/infinitylearn.com\/surge\/#organization","name":"Infinity Learn","url":"https:\/\/infinitylearn.com\/surge\/","sameAs":["https:\/\/www.facebook.com\/InfinityLearn.SriChaitanya\/","https:\/\/www.instagram.com\/infinitylearn_by_srichaitanya\/","https:\/\/www.linkedin.com\/company\/infinity-learn-by-sri-chaitanya\/","https:\/\/www.youtube.com\/c\/InfinityLearnEdu","https:\/\/twitter.com\/InfinityLearn_"],"logo":{"@type":"ImageObject","@id":"https:\/\/infinitylearn.com\/surge\/#logo","inLanguage":"en-US","url":"","contentUrl":"","caption":"Infinity Learn"},"image":{"@id":"https:\/\/infinitylearn.com\/surge\/#logo"}},{"@type":"WebSite","@id":"https:\/\/infinitylearn.com\/surge\/#website","url":"https:\/\/infinitylearn.com\/surge\/","name":"Infinity Learn by Sri Chaitanya","description":"Surge","publisher":{"@id":"https:\/\/infinitylearn.com\/surge\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/infinitylearn.com\/surge\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"en-US"},{"@type":"WebPage","@id":"https:\/\/infinitylearn.com\/surge\/question\/physics\/at-a-point-above-the-surface-of-the-earth-the-gravitational\/#webpage","url":"https:\/\/infinitylearn.com\/surge\/question\/physics\/at-a-point-above-the-surface-of-the-earth-the-gravitational\/","name":"At a point above the surface of the earth, the gravitational potential is\u00a0\u22125.12\u00d7107Jkg\u22121\u00a0and the acceleration due to gravity is\u00a06.4\u00a0ms\u22122.\u00a0Assuming the mean radius of the earth to be\u00a06400 km, the height of this point above the earth's surface is. - Infinity Learn by Sri Chaitanya","isPartOf":{"@id":"https:\/\/infinitylearn.com\/surge\/#website"},"datePublished":"2022-09-10T07:42:41+00:00","dateModified":"2022-09-10T07:42:41+00:00","description":"At a point above the surface of the earth, the gravitational potential is\u00a0\u22125.12\u00d7107Jkg\u22121\u00a0and the acceleration due to gravity is\u00a06.4\u00a0ms\u22122.\u00a0Assuming the mean radius of the earth to be\u00a06400 km, the height of this point above the earth's surface is.","breadcrumb":{"@id":"https:\/\/infinitylearn.com\/surge\/question\/physics\/at-a-point-above-the-surface-of-the-earth-the-gravitational\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/infinitylearn.com\/surge\/question\/physics\/at-a-point-above-the-surface-of-the-earth-the-gravitational\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/infinitylearn.com\/surge\/question\/physics\/at-a-point-above-the-surface-of-the-earth-the-gravitational\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/infinitylearn.com\/surge\/"},{"@type":"ListItem","position":2,"name":"At a point above the surface of the earth, the gravitational potential is\u00a0\u22125.12\u00d7107Jkg\u22121\u00a0and the acceleration due to gravity is\u00a06.4\u00a0ms\u22122.\u00a0Assuming the mean radius of the earth to be\u00a06400 km, the height of this point above the earth’s surface is."}]}]}},"_links":{"self":[{"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/questions\/264358"}],"collection":[{"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/questions"}],"about":[{"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/types\/questions"}],"author":[{"embeddable":true,"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/users\/1"}],"wp:attachment":[{"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/media?parent=264358"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/categories?post=264358"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}