{"id":88069,"date":"2025-06-01T07:00:51","date_gmt":"2025-06-01T07:00:51","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=88069"},"modified":"2025-06-01T07:00:51","modified_gmt":"2025-06-01T07:00:51","slug":"a-metallic-bob-x-of-mass-m-is-released-from-position-a-it-collides-el","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/a-metallic-bob-x-of-mass-m-is-released-from-position-a-it-collides-el\/","title":{"rendered":"A metallic bob X of mass m is released from position A. It collides el"},"content":{"rendered":"<p>A metallic bob X of mass m is released from position A. It collides elastically with another identical bob Y placed at rest at position B on a horizontal frictionless table. The angle AOB is 30\u00b0. How high does the bob X rise immediately after the collision?<\/p>\n<p>[amp_mcq option1=&#8221;To the same height as that of position A on the other side in the same trajectory&#8221; option2=&#8221;To half the height as that of position A on the other side along the same trajectory&#8221; option3=&#8221;The same height at position A&#8221; option4=&#8221;It stops at position B&#8221; correct=&#8221;option4&#8243;]<\/p>\n<div class=\"psc-box-pyq-exam-year-detail\">\n<div class=\"pyq-exam\">\n<div class=\"psc-heading\">This question was previously asked in<\/div>\n<div class=\"psc-title line-ellipsis\">UPSC NDA-1 &#8211; 2024<\/div>\n<\/div>\n<div class=\"pyq-exam-psc-buttons\"><a href=\"\/pyq\/pyq-upsc-nda-1-2024.pdf\" target=\"_blank\" class=\"psc-pdf-button\" rel=\"noopener\">Download PDF<\/a><a href=\"\/pyq-upsc-nda-1-2024\" target=\"_blank\" class=\"psc-attempt-button\" rel=\"noopener\">Attempt Online<\/a><\/div>\n<\/div>\n<section id=\"pyq-correct-answer\">\nImmediately after the collision, bob X stops at position B.<br \/>\n<\/section>\n<section id=\"pyq-key-points\">\n&#8211; The collision is described as **elastic**. In an elastic collision, both momentum and kinetic energy are conserved.<br \/>\n&#8211; The colliding bobs are **identical**, meaning they have the same mass (m).<br \/>\n&#8211; Bob Y is **at rest** at position B before the collision. Bob X has a certain velocity (V) just before the collision at B due to its swing from A.<br \/>\n&#8211; For a head-on elastic collision between two objects of equal mass where one object is initially at rest, the moving object comes to rest, and the stationary object moves off with the initial velocity of the moving object.<br \/>\n<\/section>\n<section id=\"pyq-additional-information\">\nLet $v_{Xi}$ and $v_{Yi}$ be the initial velocities of bob X and Y respectively, and $v_{Xf}$ and $v_{Yf}$ be their final velocities after the collision.<br \/>\nInitial state: $v_{Xi} = V$, $v_{Yi} = 0$.<br \/>\nConservation of Momentum: $m v_{Xi} + m v_{Yi} = m v_{Xf} + m v_{Yf} \\implies m V + 0 = m v_{Xf} + m v_{Yf} \\implies V = v_{Xf} + v_{Yf}$.<br \/>\nConservation of Kinetic Energy: $\\frac{1}{2} m v_{Xi}^2 + \\frac{1}{2} m v_{Yi}^2 = \\frac{1}{2} m v_{Xf}^2 + \\frac{1}{2} m v_{Yf}^2 \\implies \\frac{1}{2} m V^2 + 0 = \\frac{1}{2} m v_{Xf}^2 + \\frac{1}{2} m v_{Yf}^2 \\implies V^2 = v_{Xf}^2 + v_{Yf}^2$.<br \/>\nFrom the momentum equation, $v_{Yf} = V &#8211; v_{Xf}$. Substituting into the energy equation:<br \/>\n$V^2 = v_{Xf}^2 + (V &#8211; v_{Xf})^2 = v_{Xf}^2 + V^2 &#8211; 2Vv_{Xf} + v_{Xf}^2$<br \/>\n$0 = 2v_{Xf}^2 &#8211; 2Vv_{Xf} = 2v_{Xf}(v_{Xf} &#8211; V)$.<br \/>\nThis gives two possible solutions for $v_{Xf}$: $v_{Xf} = 0$ or $v_{Xf} = V$.<br \/>\nIf $v_{Xf} = V$, then $v_{Yf} = V &#8211; V = 0$, which means no collision occurred (they passed through each other, which is not the case).<br \/>\nTherefore, the physical solution is $v_{Xf} = 0$.<br \/>\nIf $v_{Xf} = 0$, then $v_{Yf} = V &#8211; 0 = V$.<br \/>\nSo, bob X stops ($v_{Xf}=0$) and bob Y moves off with velocity $V$ ($v_{Yf}=V$).<br \/>\nSince bob X stops at position B, it does not rise to any height immediately after the collision.<br \/>\n<\/section>\n","protected":false},"excerpt":{"rendered":"<p>A metallic bob X of mass m is released from position A. It collides elastically with another identical bob Y placed at rest at position B on a horizontal frictionless table. The angle AOB is 30\u00b0. How high does the bob X rise immediately after the collision? [amp_mcq option1=&#8221;To the same height as that of &#8230; <\/p>\n<p class=\"read-more-container\"><a title=\"A metallic bob X of mass m is released from position A. It collides el\" class=\"read-more button\" href=\"https:\/\/exam.pscnotes.com\/mcq\/a-metallic-bob-x-of-mass-m-is-released-from-position-a-it-collides-el\/#more-88069\">Detailed Solution<span class=\"screen-reader-text\">A metallic bob X of mass m is released from position A. It collides el<\/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":[1103,1129,1128],"class_list":["post-88069","post","type-post","status-publish","format-standard","hentry","category-upsc-nda-1","tag-1103","tag-mechanics","tag-physics","no-featured-image-padding"],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v22.2 (Yoast SEO v23.3) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>A metallic bob X of mass m is released from position A. It collides el<\/title>\n<meta name=\"description\" content=\"Immediately after the collision, bob X stops at position B. - The collision is described as **elastic**. In an elastic collision, both momentum and kinetic energy are conserved. - The colliding bobs are **identical**, meaning they have the same mass (m). - Bob Y is **at rest** at position B before the collision. Bob X has a certain velocity (V) just before the collision at B due to its swing from A. - For a head-on elastic collision between two objects of equal mass where one object is initially at rest, the moving object comes to rest, and the stationary object moves off with the initial velocity of the moving object.\" \/>\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\/a-metallic-bob-x-of-mass-m-is-released-from-position-a-it-collides-el\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"A metallic bob X of mass m is released from position A. It collides el\" \/>\n<meta property=\"og:description\" content=\"Immediately after the collision, bob X stops at position B. - The collision is described as **elastic**. In an elastic collision, both momentum and kinetic energy are conserved. - The colliding bobs are **identical**, meaning they have the same mass (m). - Bob Y is **at rest** at position B before the collision. Bob X has a certain velocity (V) just before the collision at B due to its swing from A. - For a head-on elastic collision between two objects of equal mass where one object is initially at rest, the moving object comes to rest, and the stationary object moves off with the initial velocity of the moving object.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/exam.pscnotes.com\/mcq\/a-metallic-bob-x-of-mass-m-is-released-from-position-a-it-collides-el\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ and Quiz for Exams\" \/>\n<meta property=\"article:published_time\" content=\"2025-06-01T07:00:51+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=\"2 minutes\" \/>\n<!-- \/ Yoast SEO Premium plugin. -->","yoast_head_json":{"title":"A metallic bob X of mass m is released from position A. It collides el","description":"Immediately after the collision, bob X stops at position B. - The collision is described as **elastic**. In an elastic collision, both momentum and kinetic energy are conserved. - The colliding bobs are **identical**, meaning they have the same mass (m). - Bob Y is **at rest** at position B before the collision. Bob X has a certain velocity (V) just before the collision at B due to its swing from A. - For a head-on elastic collision between two objects of equal mass where one object is initially at rest, the moving object comes to rest, and the stationary object moves off with the initial velocity of the moving object.","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\/a-metallic-bob-x-of-mass-m-is-released-from-position-a-it-collides-el\/","og_locale":"en_US","og_type":"article","og_title":"A metallic bob X of mass m is released from position A. It collides el","og_description":"Immediately after the collision, bob X stops at position B. - The collision is described as **elastic**. In an elastic collision, both momentum and kinetic energy are conserved. - The colliding bobs are **identical**, meaning they have the same mass (m). - Bob Y is **at rest** at position B before the collision. Bob X has a certain velocity (V) just before the collision at B due to its swing from A. - For a head-on elastic collision between two objects of equal mass where one object is initially at rest, the moving object comes to rest, and the stationary object moves off with the initial velocity of the moving object.","og_url":"https:\/\/exam.pscnotes.com\/mcq\/a-metallic-bob-x-of-mass-m-is-released-from-position-a-it-collides-el\/","og_site_name":"MCQ and Quiz for Exams","article_published_time":"2025-06-01T07:00:51+00:00","author":"rawan239","twitter_card":"summary_large_image","twitter_misc":{"Written by":"rawan239","Est. reading time":"2 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/exam.pscnotes.com\/mcq\/a-metallic-bob-x-of-mass-m-is-released-from-position-a-it-collides-el\/","url":"https:\/\/exam.pscnotes.com\/mcq\/a-metallic-bob-x-of-mass-m-is-released-from-position-a-it-collides-el\/","name":"A metallic bob X of mass m is released from position A. It collides el","isPartOf":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#website"},"datePublished":"2025-06-01T07:00:51+00:00","dateModified":"2025-06-01T07:00:51+00:00","author":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209"},"description":"Immediately after the collision, bob X stops at position B. - The collision is described as **elastic**. In an elastic collision, both momentum and kinetic energy are conserved. - The colliding bobs are **identical**, meaning they have the same mass (m). - Bob Y is **at rest** at position B before the collision. Bob X has a certain velocity (V) just before the collision at B due to its swing from A. - For a head-on elastic collision between two objects of equal mass where one object is initially at rest, the moving object comes to rest, and the stationary object moves off with the initial velocity of the moving object.","breadcrumb":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/a-metallic-bob-x-of-mass-m-is-released-from-position-a-it-collides-el\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/exam.pscnotes.com\/mcq\/a-metallic-bob-x-of-mass-m-is-released-from-position-a-it-collides-el\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/exam.pscnotes.com\/mcq\/a-metallic-bob-x-of-mass-m-is-released-from-position-a-it-collides-el\/#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":"A metallic bob X of mass m is released from position A. It collides el"}]},{"@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\/88069","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=88069"}],"version-history":[{"count":0,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts\/88069\/revisions"}],"wp:attachment":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/media?parent=88069"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/categories?post=88069"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/tags?post=88069"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}