{"id":87349,"date":"2025-06-01T06:41:26","date_gmt":"2025-06-01T06:41:26","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=87349"},"modified":"2025-06-01T06:41:26","modified_gmt":"2025-06-01T06:41:26","slug":"suppose-the-force-of-gravitation-between-two-equal-masses-is-f-if-eac","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/suppose-the-force-of-gravitation-between-two-equal-masses-is-f-if-eac\/","title":{"rendered":"Suppose the force of gravitation between two equal masses is F. If eac"},"content":{"rendered":"

Suppose the force of gravitation between two equal masses is F. If each mass is doubled keeping the distance of separation between them unchanged, the force would become<\/p>\n

[amp_mcq option1=”F” option2=”2 F” option3=”4 F” option4=”” correct=”option3″]<\/p>\n

\n
\n
This question was previously asked in<\/div>\n
UPSC NDA-1 – 2016<\/div>\n<\/div>\n
Download PDF<\/a>Attempt Online<\/a><\/div>\n<\/div>\n
According to Newton’s Law of Universal Gravitation, the force of gravitation (F) between two masses (m\u2081 and m\u2082) separated by a distance (r) is given by the formula:
\nF = G * (m\u2081 * m\u2082) \/ r\u00b2
\nwhere G is the gravitational constant.
\nInitially, we have two equal masses, let’s call them m. So, m\u2081 = m and m\u2082 = m. The force is F = G * (m * m) \/ r\u00b2 = G * m\u00b2 \/ r\u00b2.
\nNow, each mass is doubled, so the new masses are m\u2081’ = 2m and m\u2082’ = 2m. The distance of separation (r) remains unchanged.
\nThe new force (F’) is:
\nF’ = G * (m\u2081’ * m\u2082’) \/ r\u00b2
\nF’ = G * (2m * 2m) \/ r\u00b2
\nF’ = G * (4 * m\u00b2) \/ r\u00b2
\nWe can rewrite this as:
\nF’ = 4 * (G * m\u00b2 \/ r\u00b2)
\nSince F = G * m\u00b2 \/ r\u00b2, we have F’ = 4 * F.
\nThe force becomes four times the original force.<\/section>\n
The gravitational force between two masses is directly proportional to the product of their masses. If both masses are doubled, their product becomes (2m) * (2m) = 4m\u00b2, quadrupling the force, assuming the distance remains constant.<\/section>\n
The gravitational force is also inversely proportional to the square of the distance between the centres of the masses. If the distance were, for example, doubled instead of the masses, the force would become F\/4.<\/section>\n","protected":false},"excerpt":{"rendered":"

Suppose the force of gravitation between two equal masses is F. If each mass is doubled keeping the distance of separation between them unchanged, the force would become [amp_mcq option1=”F” option2=”2 F” option3=”4 F” option4=”” correct=”option3″] This question was previously asked in UPSC NDA-1 – 2016 Download PDFAttempt Online According to Newton’s Law of Universal … <\/p>\n

Detailed SolutionSuppose the force of gravitation between two equal masses is F. If eac<\/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":[1093],"tags":[1098,1129,1128],"class_list":["post-87349","post","type-post","status-publish","format-standard","hentry","category-upsc-nda-1","tag-1098","tag-mechanics","tag-physics","no-featured-image-padding"],"yoast_head":"\nSuppose the force of gravitation between two equal masses is F. If eac<\/title>\n<meta name=\"description\" content=\"According to Newton's Law of Universal Gravitation, the force of gravitation (F) between two masses (m\u2081 and m\u2082) separated by a distance (r) is given by the formula: F = G * (m\u2081 * m\u2082) \/ r\u00b2 where G is the gravitational constant. Initially, we have two equal masses, let's call them m. So, m\u2081 = m and m\u2082 = m. The force is F = G * (m * m) \/ r\u00b2 = G * m\u00b2 \/ r\u00b2. Now, each mass is doubled, so the new masses are m\u2081' = 2m and m\u2082' = 2m. The distance of separation (r) remains unchanged. The new force (F') is: F' = G * (m\u2081' * m\u2082') \/ r\u00b2 F' = G * (2m * 2m) \/ r\u00b2 F' = G * (4 * m\u00b2) \/ r\u00b2 We can rewrite this as: F' = 4 * (G * m\u00b2 \/ r\u00b2) Since F = G * m\u00b2 \/ r\u00b2, we have F' = 4 * F. The force becomes four times the original force. The gravitational force between two masses is directly proportional to the product of their masses. If both masses are doubled, their product becomes (2m) * (2m) = 4m\u00b2, quadrupling the force, assuming the distance remains constant.\" \/>\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\/suppose-the-force-of-gravitation-between-two-equal-masses-is-f-if-eac\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Suppose the force of gravitation between two equal masses is F. If eac\" \/>\n<meta property=\"og:description\" content=\"According to Newton's Law of Universal Gravitation, the force of gravitation (F) between two masses (m\u2081 and m\u2082) separated by a distance (r) is given by the formula: F = G * (m\u2081 * m\u2082) \/ r\u00b2 where G is the gravitational constant. Initially, we have two equal masses, let's call them m. So, m\u2081 = m and m\u2082 = m. The force is F = G * (m * m) \/ r\u00b2 = G * m\u00b2 \/ r\u00b2. Now, each mass is doubled, so the new masses are m\u2081' = 2m and m\u2082' = 2m. The distance of separation (r) remains unchanged. The new force (F') is: F' = G * (m\u2081' * m\u2082') \/ r\u00b2 F' = G * (2m * 2m) \/ r\u00b2 F' = G * (4 * m\u00b2) \/ r\u00b2 We can rewrite this as: F' = 4 * (G * m\u00b2 \/ r\u00b2) Since F = G * m\u00b2 \/ r\u00b2, we have F' = 4 * F. The force becomes four times the original force. The gravitational force between two masses is directly proportional to the product of their masses. If both masses are doubled, their product becomes (2m) * (2m) = 4m\u00b2, quadrupling the force, assuming the distance remains constant.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/exam.pscnotes.com\/mcq\/suppose-the-force-of-gravitation-between-two-equal-masses-is-f-if-eac\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ and Quiz for Exams\" \/>\n<meta property=\"article:published_time\" content=\"2025-06-01T06:41:26+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":"Suppose the force of gravitation between two equal masses is F. If eac","description":"According to Newton's Law of Universal Gravitation, the force of gravitation (F) between two masses (m\u2081 and m\u2082) separated by a distance (r) is given by the formula: F = G * (m\u2081 * m\u2082) \/ r\u00b2 where G is the gravitational constant. Initially, we have two equal masses, let's call them m. So, m\u2081 = m and m\u2082 = m. The force is F = G * (m * m) \/ r\u00b2 = G * m\u00b2 \/ r\u00b2. Now, each mass is doubled, so the new masses are m\u2081' = 2m and m\u2082' = 2m. The distance of separation (r) remains unchanged. The new force (F') is: F' = G * (m\u2081' * m\u2082') \/ r\u00b2 F' = G * (2m * 2m) \/ r\u00b2 F' = G * (4 * m\u00b2) \/ r\u00b2 We can rewrite this as: F' = 4 * (G * m\u00b2 \/ r\u00b2) Since F = G * m\u00b2 \/ r\u00b2, we have F' = 4 * F. The force becomes four times the original force. The gravitational force between two masses is directly proportional to the product of their masses. If both masses are doubled, their product becomes (2m) * (2m) = 4m\u00b2, quadrupling the force, assuming the distance remains constant.","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\/suppose-the-force-of-gravitation-between-two-equal-masses-is-f-if-eac\/","og_locale":"en_US","og_type":"article","og_title":"Suppose the force of gravitation between two equal masses is F. If eac","og_description":"According to Newton's Law of Universal Gravitation, the force of gravitation (F) between two masses (m\u2081 and m\u2082) separated by a distance (r) is given by the formula: F = G * (m\u2081 * m\u2082) \/ r\u00b2 where G is the gravitational constant. Initially, we have two equal masses, let's call them m. So, m\u2081 = m and m\u2082 = m. The force is F = G * (m * m) \/ r\u00b2 = G * m\u00b2 \/ r\u00b2. Now, each mass is doubled, so the new masses are m\u2081' = 2m and m\u2082' = 2m. The distance of separation (r) remains unchanged. The new force (F') is: F' = G * (m\u2081' * m\u2082') \/ r\u00b2 F' = G * (2m * 2m) \/ r\u00b2 F' = G * (4 * m\u00b2) \/ r\u00b2 We can rewrite this as: F' = 4 * (G * m\u00b2 \/ r\u00b2) Since F = G * m\u00b2 \/ r\u00b2, we have F' = 4 * F. The force becomes four times the original force. The gravitational force between two masses is directly proportional to the product of their masses. If both masses are doubled, their product becomes (2m) * (2m) = 4m\u00b2, quadrupling the force, assuming the distance remains constant.","og_url":"https:\/\/exam.pscnotes.com\/mcq\/suppose-the-force-of-gravitation-between-two-equal-masses-is-f-if-eac\/","og_site_name":"MCQ and Quiz for Exams","article_published_time":"2025-06-01T06:41:26+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\/suppose-the-force-of-gravitation-between-two-equal-masses-is-f-if-eac\/","url":"https:\/\/exam.pscnotes.com\/mcq\/suppose-the-force-of-gravitation-between-two-equal-masses-is-f-if-eac\/","name":"Suppose the force of gravitation between two equal masses is F. If eac","isPartOf":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#website"},"datePublished":"2025-06-01T06:41:26+00:00","dateModified":"2025-06-01T06:41:26+00:00","author":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209"},"description":"According to Newton's Law of Universal Gravitation, the force of gravitation (F) between two masses (m\u2081 and m\u2082) separated by a distance (r) is given by the formula: F = G * (m\u2081 * m\u2082) \/ r\u00b2 where G is the gravitational constant. Initially, we have two equal masses, let's call them m. So, m\u2081 = m and m\u2082 = m. The force is F = G * (m * m) \/ r\u00b2 = G * m\u00b2 \/ r\u00b2. Now, each mass is doubled, so the new masses are m\u2081' = 2m and m\u2082' = 2m. The distance of separation (r) remains unchanged. The new force (F') is: F' = G * (m\u2081' * m\u2082') \/ r\u00b2 F' = G * (2m * 2m) \/ r\u00b2 F' = G * (4 * m\u00b2) \/ r\u00b2 We can rewrite this as: F' = 4 * (G * m\u00b2 \/ r\u00b2) Since F = G * m\u00b2 \/ r\u00b2, we have F' = 4 * F. The force becomes four times the original force. The gravitational force between two masses is directly proportional to the product of their masses. If both masses are doubled, their product becomes (2m) * (2m) = 4m\u00b2, quadrupling the force, assuming the distance remains constant.","breadcrumb":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/suppose-the-force-of-gravitation-between-two-equal-masses-is-f-if-eac\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/exam.pscnotes.com\/mcq\/suppose-the-force-of-gravitation-between-two-equal-masses-is-f-if-eac\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/exam.pscnotes.com\/mcq\/suppose-the-force-of-gravitation-between-two-equal-masses-is-f-if-eac\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/exam.pscnotes.com\/mcq\/"},{"@type":"ListItem","position":2,"name":"UPSC NDA-1","item":"https:\/\/exam.pscnotes.com\/mcq\/category\/upsc-nda-1\/"},{"@type":"ListItem","position":3,"name":"Suppose the force of gravitation between two equal masses is F. 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