{"id":246012,"date":"2022-09-10T08:57:54","date_gmt":"2022-09-10T03:27:54","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/question\/at-what-height-from-the-surface-of-earth-the-gravitational-potential-and-the-value-of-g-are-5-4-x107-j-kg-1-and-6-0-ms-2-respectively-take-the\/"},"modified":"2022-09-10T08:57:54","modified_gmt":"2022-09-10T03:27:54","slug":"at-what-height-from-the-surface-of-earth-the-gravitational-potential-and-the-value-of-g-are-5-4-x107-j-kg-1-and-6-0-ms-2-respectively-take-the","status":"publish","type":"questions","link":"https:\/\/infinitylearn.com\/surge\/question\/physics\/at-what-height-from-the-surface-of-earth-the-gravitational\/","title":{"rendered":"At what height from the surface of Earth, the gravitational potential and the value of\u00a0g\u00a0are\u00a0-5.4\u00a0\u00d7107\u00a0J\u00a0kg-1\u00a0and\u00a06.0\u00a0ms-2\u00a0respectively? Take the radius of Earth as\u00a06400\u00a0km."},"content":{"rendered":"","protected":false},"author":1,"template":"","meta":{"_yoast_wpseo_focuskw":"","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"At what height from the surface of Earth, the gravitational potential and the value of\u00a0g\u00a0are\u00a0-5.4\u00a0\u00d7107\u00a0J\u00a0kg-1\u00a0and\u00a06.0\u00a0ms-2\u00a0respectively? Take the radius of Earth as\u00a06400\u00a0km.","custom_permalink":"question\/physics\/at-what-height-from-the-surface-of-earth-the-gravitational\/"},"categories":[],"acf":{"question":"

At what height from the surface of Earth, the gravitational potential and the value of g<\/mi><\/math> are -<\/mo>5<\/mn>.<\/mo>4<\/mn> <\/mo>\u00d7<\/mo>10<\/mn>7<\/mn><\/msup> <\/mo>J<\/mi> <\/mo>kg<\/mi>-<\/mo>1<\/mn><\/mrow><\/msup><\/math> and 6<\/mn>.<\/mo>0<\/mn> <\/mo>ms<\/mi>-<\/mo>2<\/mn><\/mrow><\/msup><\/math> respectively? Take the radius of Earth as 6400<\/mn> <\/mo>km<\/mi><\/math>.<\/p>","options":[{"option":"

1400<\/mn> <\/mo>km<\/mi><\/math><\/p>","correct":false},{"option":"

2000<\/mn> <\/mo>km<\/mi><\/math><\/p>","correct":false},{"option":"

2600<\/mn> <\/mo>km<\/mi><\/math><\/p>","correct":true},{"option":"

1600<\/mn> <\/mo>km<\/mi><\/math><\/p>","correct":false}],"solution":"

Gravitation potential at a height h<\/mi><\/math> from the surface of Earth, V<\/mi>h<\/mi><\/msub>=<\/mo>-<\/mo>5<\/mn>.<\/mo>4<\/mn> <\/mo>\u00d7<\/mo>10<\/mn>7<\/mn><\/msup> <\/mo>J<\/mi> <\/mo>kg<\/mi>-<\/mo>1<\/mn><\/mrow><\/msup><\/math><\/p>

At the same point acceleration due to gravity, g<\/mi>h<\/mi><\/msub>=<\/mo>6<\/mn> <\/mo>m<\/mi> <\/mo>s<\/mi>-<\/mo>2<\/mn><\/mrow><\/msup><\/math><\/p>

R<\/mi> <\/mo>=<\/mo>6400<\/mn> <\/mo>km<\/mi>=<\/mo> <\/mo>6<\/mn>.<\/mo>4<\/mn>\u00d7<\/mo>10<\/mn>6<\/mn><\/msup>m<\/mi><\/math><\/p>

We know, V<\/mi>h<\/mi><\/msub>=<\/mo>-<\/mo>G<\/mi>M<\/mi><\/mrow>R<\/mi>+<\/mo>h<\/mi><\/mrow><\/mfenced><\/mfrac><\/math><\/p>

g<\/mi>h<\/mi><\/msub>=<\/mo>G<\/mi>M<\/mi><\/mrow>R<\/mi>+<\/mo>h<\/mi><\/mrow><\/mfenced>2<\/mn><\/msup><\/mfrac>=<\/mo>-<\/mo>V<\/mi>h<\/mi><\/msub>R<\/mi>+<\/mo>h<\/mi><\/mrow><\/mfrac> <\/mspace>\u21d2<\/mo>R<\/mi>+<\/mo>h<\/mi>=<\/mo>-<\/mo>V<\/mi>h<\/mi><\/msub>g<\/mi>h<\/mi><\/msub><\/mfrac> <\/mspace>\u2234<\/mo> <\/mo> <\/mo> <\/mo>h<\/mi>=<\/mo>-<\/mo>V<\/mi>h<\/mi><\/msub>g<\/mi>h<\/mi><\/msub><\/mfrac>-<\/mo>R<\/mi>=<\/mo>-<\/mo>-<\/mo>5<\/mn>.<\/mo>4<\/mn>\u00d7<\/mo>10<\/mn>7<\/mn><\/msup><\/mrow><\/mfenced>6<\/mn><\/mfrac>-<\/mo>6<\/mn>.<\/mo>4<\/mn>\u00d7<\/mo>10<\/mn>6<\/mn><\/msup> <\/mspace> <\/mo> <\/mo> <\/mo> <\/mo> <\/mo> <\/mo> <\/mo>=<\/mo>9<\/mn>\u00d7<\/mo>10<\/mn>6<\/mn><\/msup>-<\/mo>6<\/mn>.<\/mo>4<\/mn>\u00d7<\/mo>10<\/mn>6<\/mn><\/msup>=<\/mo>2600<\/mn> <\/mo>km<\/mi><\/math><\/p>","subject":""},"yoast_head":"\nAt what height from the surface of Earth, the gravitational potential and the value of\u00a0g\u00a0are\u00a0-5.4\u00a0\u00d7107\u00a0J\u00a0kg-1\u00a0and\u00a06.0\u00a0ms-2\u00a0respectively? Take the radius of Earth as\u00a06400\u00a0km. - Infinity Learn by Sri Chaitanya<\/title>\n<meta name=\"description\" content=\"At what height from the surface of Earth, the gravitational potential and the value of\u00a0g\u00a0are\u00a0-5.4\u00a0\u00d7107\u00a0J\u00a0kg-1\u00a0and\u00a06.0\u00a0ms-2\u00a0respectively? Take the radius of Earth as\u00a06400\u00a0km.\" \/>\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-what-height-from-the-surface-of-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 what height from the surface of Earth, the gravitational potential and the value of\u00a0g\u00a0are\u00a0-5.4\u00a0\u00d7107\u00a0J\u00a0kg-1\u00a0and\u00a06.0\u00a0ms-2\u00a0respectively? 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Take the radius of Earth as\u00a06400\u00a0km. - Infinity Learn by Sri Chaitanya","description":"At what height from the surface of Earth, the gravitational potential and the value of\u00a0g\u00a0are\u00a0-5.4\u00a0\u00d7107\u00a0J\u00a0kg-1\u00a0and\u00a06.0\u00a0ms-2\u00a0respectively? Take the radius of Earth as\u00a06400\u00a0km.","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-what-height-from-the-surface-of-earth-the-gravitational\/","og_locale":"en_US","og_type":"article","og_title":"At what height from the surface of Earth, the gravitational potential and the value of\u00a0g\u00a0are\u00a0-5.4\u00a0\u00d7107\u00a0J\u00a0kg-1\u00a0and\u00a06.0\u00a0ms-2\u00a0respectively? Take the radius of Earth as\u00a06400\u00a0km. - Infinity Learn by Sri Chaitanya","og_description":"At what height from the surface of Earth, the gravitational potential and the value of\u00a0g\u00a0are\u00a0-5.4\u00a0\u00d7107\u00a0J\u00a0kg-1\u00a0and\u00a06.0\u00a0ms-2\u00a0respectively? 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Take the radius of Earth as\u00a06400\u00a0km. - Infinity Learn by Sri Chaitanya","isPartOf":{"@id":"https:\/\/infinitylearn.com\/surge\/#website"},"datePublished":"2022-09-10T03:27:54+00:00","dateModified":"2022-09-10T03:27:54+00:00","description":"At what height from the surface of Earth, the gravitational potential and the value of\u00a0g\u00a0are\u00a0-5.4\u00a0\u00d7107\u00a0J\u00a0kg-1\u00a0and\u00a06.0\u00a0ms-2\u00a0respectively? 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