{"id":86401,"date":"2025-06-01T03:46:12","date_gmt":"2025-06-01T03:46:12","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=86401"},"modified":"2025-06-01T03:46:12","modified_gmt":"2025-06-01T03:46:12","slug":"if-the-moon-is-brought-closer-to-the-earth-such-that-its-distance-from","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/if-the-moon-is-brought-closer-to-the-earth-such-that-its-distance-from\/","title":{"rendered":"If the Moon is brought closer to the Earth such that its distance from"},"content":{"rendered":"

If the Moon is brought closer to the Earth such that its distance from the Earth becomes half of the original distance, then the gravitational force of attraction between the Earth and the Moon would :<\/p>\n

[amp_mcq option1=”reduce to half of its original value.” option2=”increase to two times of its original value.” option3=”remain the same as the original value.” option4=”increase to four times of its original value.” correct=”option4″]<\/p>\n

\n
\n
This question was previously asked in<\/div>\n
UPSC CDS-2 – 2023<\/div>\n<\/div>\n
Download PDF<\/a>Attempt Online<\/a><\/div>\n<\/div>\n
\nThe correct answer is D) increase to four times of its original value.
\n<\/section>\n
\nAccording to Newton’s Law of Universal Gravitation, the gravitational force (F) between two objects with masses M\u2081 and M\u2082 is directly proportional to the product of their masses and inversely proportional to the square of the distance (r) between their centers: F = G * (M\u2081 * M\u2082) \/ r\u00b2.
\nIn this case, M\u2081 is the mass of the Earth (M_earth) and M\u2082 is the mass of the Moon (M_moon). Let the original distance be r. The original gravitational force is F = G * (M_earth * M_moon) \/ r\u00b2.
\nIf the distance is halved, the new distance is r’ = r\/2. The new gravitational force F’ will be:
\nF’ = G * (M_earth * M_moon) \/ (r’)\u00b2
\nF’ = G * (M_earth * M_moon) \/ (r\/2)\u00b2
\nF’ = G * (M_earth * M_moon) \/ (r\u00b2\/4)
\nF’ = 4 * [G * (M_earth * M_moon) \/ r\u00b2]
\nSo, F’ = 4 * F. The gravitational force increases to four times its original value.
\n<\/section>\n
\nThis inverse square relationship means that if the distance is reduced by a factor, the force increases by the square of that factor. Conversely, if the distance were doubled, the force would reduce to (1\/2)\u00b2, or one-fourth, of its original value. This law governs gravitational interactions throughout the universe.
\n<\/section>\n","protected":false},"excerpt":{"rendered":"

If the Moon is brought closer to the Earth such that its distance from the Earth becomes half of the original distance, then the gravitational force of attraction between the Earth and the Moon would : [amp_mcq option1=”reduce to half of its original value.” option2=”increase to two times of its original value.” option3=”remain the same … <\/p>\n

Detailed SolutionIf the Moon is brought closer to the Earth such that its distance from<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1088],"tags":[1105,1129,1128],"class_list":["post-86401","post","type-post","status-publish","format-standard","hentry","category-upsc-cds-2","tag-1105","tag-mechanics","tag-physics","no-featured-image-padding"],"yoast_head":"\nIf the Moon is brought closer to the Earth such that its distance from<\/title>\n<meta name=\"description\" content=\"The correct answer is D) increase to four times of its original value. According to Newton's Law of Universal Gravitation, the gravitational force (F) between two objects with masses M\u2081 and M\u2082 is directly proportional to the product of their masses and inversely proportional to the square of the distance (r) between their centers: F = G * (M\u2081 * M\u2082) \/ r\u00b2. In this case, M\u2081 is the mass of the Earth (M_earth) and M\u2082 is the mass of the Moon (M_moon). Let the original distance be r. The original gravitational force is F = G * (M_earth * M_moon) \/ r\u00b2. If the distance is halved, the new distance is r' = r\/2. The new gravitational force F' will be: F' = G * (M_earth * M_moon) \/ (r')\u00b2 F' = G * (M_earth * M_moon) \/ (r\/2)\u00b2 F' = G * (M_earth * M_moon) \/ (r\u00b2\/4) F' = 4 * [G * (M_earth * M_moon) \/ r\u00b2] So, F' = 4 * F. The gravitational force increases to four times its original value.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/exam.pscnotes.com\/mcq\/if-the-moon-is-brought-closer-to-the-earth-such-that-its-distance-from\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"If the Moon is brought closer to the Earth such that its distance from\" \/>\n<meta property=\"og:description\" content=\"The correct answer is D) increase to four times of its original value. According to Newton's Law of Universal Gravitation, the gravitational force (F) between two objects with masses M\u2081 and M\u2082 is directly proportional to the product of their masses and inversely proportional to the square of the distance (r) between their centers: F = G * (M\u2081 * M\u2082) \/ r\u00b2. In this case, M\u2081 is the mass of the Earth (M_earth) and M\u2082 is the mass of the Moon (M_moon). Let the original distance be r. The original gravitational force is F = G * (M_earth * M_moon) \/ r\u00b2. If the distance is halved, the new distance is r' = r\/2. The new gravitational force F' will be: F' = G * (M_earth * M_moon) \/ (r')\u00b2 F' = G * (M_earth * M_moon) \/ (r\/2)\u00b2 F' = G * (M_earth * M_moon) \/ (r\u00b2\/4) F' = 4 * [G * (M_earth * M_moon) \/ r\u00b2] So, F' = 4 * F. The gravitational force increases to four times its original value.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/exam.pscnotes.com\/mcq\/if-the-moon-is-brought-closer-to-the-earth-such-that-its-distance-from\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ and Quiz for Exams\" \/>\n<meta property=\"article:published_time\" content=\"2025-06-01T03:46:12+00:00\" \/>\n<meta name=\"author\" content=\"rawan239\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"rawan239\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 minute\" \/>\n<!-- \/ Yoast SEO Premium plugin. -->","yoast_head_json":{"title":"If the Moon is brought closer to the Earth such that its distance from","description":"The correct answer is D) increase to four times of its original value. According to Newton's Law of Universal Gravitation, the gravitational force (F) between two objects with masses M\u2081 and M\u2082 is directly proportional to the product of their masses and inversely proportional to the square of the distance (r) between their centers: F = G * (M\u2081 * M\u2082) \/ r\u00b2. In this case, M\u2081 is the mass of the Earth (M_earth) and M\u2082 is the mass of the Moon (M_moon). Let the original distance be r. The original gravitational force is F = G * (M_earth * M_moon) \/ r\u00b2. If the distance is halved, the new distance is r' = r\/2. The new gravitational force F' will be: F' = G * (M_earth * M_moon) \/ (r')\u00b2 F' = G * (M_earth * M_moon) \/ (r\/2)\u00b2 F' = G * (M_earth * M_moon) \/ (r\u00b2\/4) F' = 4 * [G * (M_earth * M_moon) \/ r\u00b2] So, F' = 4 * F. The gravitational force increases to four times its original value.","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:\/\/exam.pscnotes.com\/mcq\/if-the-moon-is-brought-closer-to-the-earth-such-that-its-distance-from\/","og_locale":"en_US","og_type":"article","og_title":"If the Moon is brought closer to the Earth such that its distance from","og_description":"The correct answer is D) increase to four times of its original value. According to Newton's Law of Universal Gravitation, the gravitational force (F) between two objects with masses M\u2081 and M\u2082 is directly proportional to the product of their masses and inversely proportional to the square of the distance (r) between their centers: F = G * (M\u2081 * M\u2082) \/ r\u00b2. In this case, M\u2081 is the mass of the Earth (M_earth) and M\u2082 is the mass of the Moon (M_moon). Let the original distance be r. The original gravitational force is F = G * (M_earth * M_moon) \/ r\u00b2. If the distance is halved, the new distance is r' = r\/2. The new gravitational force F' will be: F' = G * (M_earth * M_moon) \/ (r')\u00b2 F' = G * (M_earth * M_moon) \/ (r\/2)\u00b2 F' = G * (M_earth * M_moon) \/ (r\u00b2\/4) F' = 4 * [G * (M_earth * M_moon) \/ r\u00b2] So, F' = 4 * F. The gravitational force increases to four times its original value.","og_url":"https:\/\/exam.pscnotes.com\/mcq\/if-the-moon-is-brought-closer-to-the-earth-such-that-its-distance-from\/","og_site_name":"MCQ and Quiz for Exams","article_published_time":"2025-06-01T03:46:12+00:00","author":"rawan239","twitter_card":"summary_large_image","twitter_misc":{"Written by":"rawan239","Est. reading time":"1 minute"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/exam.pscnotes.com\/mcq\/if-the-moon-is-brought-closer-to-the-earth-such-that-its-distance-from\/","url":"https:\/\/exam.pscnotes.com\/mcq\/if-the-moon-is-brought-closer-to-the-earth-such-that-its-distance-from\/","name":"If the Moon is brought closer to the Earth such that its distance from","isPartOf":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#website"},"datePublished":"2025-06-01T03:46:12+00:00","dateModified":"2025-06-01T03:46:12+00:00","author":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209"},"description":"The correct answer is D) increase to four times of its original value. According to Newton's Law of Universal Gravitation, the gravitational force (F) between two objects with masses M\u2081 and M\u2082 is directly proportional to the product of their masses and inversely proportional to the square of the distance (r) between their centers: F = G * (M\u2081 * M\u2082) \/ r\u00b2. In this case, M\u2081 is the mass of the Earth (M_earth) and M\u2082 is the mass of the Moon (M_moon). Let the original distance be r. The original gravitational force is F = G * (M_earth * M_moon) \/ r\u00b2. If the distance is halved, the new distance is r' = r\/2. The new gravitational force F' will be: F' = G * (M_earth * M_moon) \/ (r')\u00b2 F' = G * (M_earth * M_moon) \/ (r\/2)\u00b2 F' = G * (M_earth * M_moon) \/ (r\u00b2\/4) F' = 4 * [G * (M_earth * M_moon) \/ r\u00b2] So, F' = 4 * F. The gravitational force increases to four times its original value.","breadcrumb":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/if-the-moon-is-brought-closer-to-the-earth-such-that-its-distance-from\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/exam.pscnotes.com\/mcq\/if-the-moon-is-brought-closer-to-the-earth-such-that-its-distance-from\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/exam.pscnotes.com\/mcq\/if-the-moon-is-brought-closer-to-the-earth-such-that-its-distance-from\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/exam.pscnotes.com\/mcq\/"},{"@type":"ListItem","position":2,"name":"UPSC CDS-2","item":"https:\/\/exam.pscnotes.com\/mcq\/category\/upsc-cds-2\/"},{"@type":"ListItem","position":3,"name":"If the Moon is brought closer to the Earth such that its distance from"}]},{"@type":"WebSite","@id":"https:\/\/exam.pscnotes.com\/mcq\/#website","url":"https:\/\/exam.pscnotes.com\/mcq\/","name":"MCQ and Quiz for Exams","description":"","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/exam.pscnotes.com\/mcq\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"en-US"},{"@type":"Person","@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209","name":"rawan239","image":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/image\/","url":"https:\/\/secure.gravatar.com\/avatar\/761a7274f9cce048fa5b921221e7934820d74514df93ef195a9d22af0c1c9001?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/761a7274f9cce048fa5b921221e7934820d74514df93ef195a9d22af0c1c9001?s=96&d=mm&r=g","caption":"rawan239"},"sameAs":["https:\/\/exam.pscnotes.com"],"url":"https:\/\/exam.pscnotes.com\/mcq\/author\/rawan239\/"}]}},"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts\/86401","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/comments?post=86401"}],"version-history":[{"count":0,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts\/86401\/revisions"}],"wp:attachment":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/media?parent=86401"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/categories?post=86401"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/tags?post=86401"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}