{"id":6717,"date":"2024-04-15T02:33:07","date_gmt":"2024-04-15T02:33:07","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=6717"},"modified":"2024-04-15T02:33:07","modified_gmt":"2024-04-15T02:33:07","slug":"the-masses-of-two-balls-are-in-the-ratio-of-2-1-and-their-respective-velocities-are-in-the-ratio-of-1-2-but-in-opposite-direction-before-impact-if-the-coefficient-of-restitution-is-frac12","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/the-masses-of-two-balls-are-in-the-ratio-of-2-1-and-their-respective-velocities-are-in-the-ratio-of-1-2-but-in-opposite-direction-before-impact-if-the-coefficient-of-restitution-is-frac12\/","title":{"rendered":"The masses of two balls are in the ratio of 2 : 1 and their respective velocities are in the ratio of 1 : 2 but in opposite direction before impact. If the coefficient of restitution is $$\\frac{1}{2}$$, the velocities of separation of the balls will be equal to A. Original velocity in the same direction B. Half the original velocity in the same direction C. Half the original velocity in the opposite direction D. Original velocity in the opposite direction"},"content":{"rendered":"<p>\r\n    <!-- Check if it's an AMP page -->\r\n            <!-- Non-AMP version -->\r\n        <div class=\"mcq-container\" data-quiz-id=\"quizState_6a9b4e442a78f\">\r\n                                            <div class=\"option\" data-option-key=\"option1\" data-is-correct=\"true\">\r\n                    Original velocity in the same direction                <\/div>\r\n                                            <div class=\"option\" data-option-key=\"option2\" data-is-correct=\"false\">\r\n                    Half the original velocity in the same direction                <\/div>\r\n                                            <div class=\"option\" data-option-key=\"option3\" data-is-correct=\"false\">\r\n                    Half the original velocity in the opposite direction                <\/div>\r\n                                            <div class=\"option\" data-option-key=\"option4\" data-is-correct=\"false\">\r\n                    Original velocity in the opposite direction                <\/div>\r\n                            \r\n            <!-- Feedback messages for non-AMP -->\r\n            <div class=\"feedback\" data-feedback=\"wrong\">Answer is Right!<\/div>\r\n            <div class=\"feedback\" data-feedback=\"right\">Answer is Wrong!<\/div>\r\n        <\/div>\r\n\r\n        <script>\r\n        document.addEventListener('DOMContentLoaded', function () {\r\n            var containers = document.querySelectorAll('.mcq-container');\r\n\r\n            containers.forEach(function(container) {\r\n                var options = container.querySelectorAll('.option');\r\n                var feedbackSelect = container.querySelector('[data-feedback=\"select\"]');\r\n                var feedbackWrong = container.querySelector('[data-feedback=\"wrong\"]');\r\n                var feedbackRight = container.querySelector('[data-feedback=\"right\"]');\r\n\r\n                options.forEach(function(option) {\r\n                    option.addEventListener('click', function() {\r\n                        var selectedOption = option.getAttribute('data-option-key');\r\n                        var isCorrect = option.getAttribute('data-is-correct') === 'true';\r\n\r\n                        \/\/ Remove previous selections\r\n                        options.forEach(function(opt) {\r\n                            opt.classList.remove('correct', 'incorrect');\r\n                        });\r\n\r\n                        \/\/ Add the correct\/incorrect class\r\n                        if (isCorrect) {\r\n                            option.classList.add('correct');\r\n                            feedbackRight.hidden = false;\r\n                            feedbackWrong.hidden = true;\r\n                        } else {\r\n                            option.classList.add('incorrect');\r\n                            feedbackRight.hidden = true;\r\n                            feedbackWrong.hidden = false;\r\n                        }\r\n\r\n                        \/\/ Hide select feedback\r\n                        feedbackSelect.hidden = true;\r\n                    });\r\n                });\r\n            });\r\n        });\r\n        <\/script>\r\n    \r\n    <!--more--><\/p>\n<p>The correct answer is $\\boxed{\\text{C}}$.<\/p>\n<p>The <div class=\"telegram-channel-container\">\r\n        <a href=\"https:\/\/t.me\/pscnotes2025\" target=\"_blank\" class=\"telegram-channel-button\">\r\n            <span class=\"telegram-icon\">\r\n                <svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" viewBox=\"0 0 496 512\">\r\n                    <path fill=\"white\" d=\"M248,8C111,8,0,119,0,256s111,248,248,248s248-111,248-248S385,8,248,8z M362,177L320,367c-3,14-10,18-20,14l-56-41l-27,26 c-3,3-5,5-10,5l4-63L323,196c5-5-1-7-8-3l-98,62l-42-13c-9-3-10-9,2-14l162-63C351,160,365,164,362,177z\"\/>\r\n                <\/svg>\r\n            <\/span>\r\n            Join Our Telegram Channel\r\n        <\/a>\r\n    <\/div> coefficient of restitution is a measure of how much energy is lost in an elastic collision. A coefficient of restitution of $\\frac{1}{2}$ means that half of the energy is lost in the collision.<\/p>\n<p>In this case, the masses of the two balls are in the ratio of 2 : 1 and their respective velocities are in <div class=\"youtube-subscribe-container\">\r\n        <a href=\"https:\/\/www.youtube.com\/channel\/UCNHT8lW-JmLC68rjBfZhdkg?sub_confirmation=1\" target=\"_blank\" class=\"youtube-subscribe-button\">\r\n            <span class=\"youtube-icon\">\r\n                <svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" viewBox=\"0 0 576 512\">\r\n                    <path d=\"M549.7 124.1c-6.3-23.7-24.8-42.3-48.3-48.6C458.8 64 288 64 288 64S117.2 64 74.6 75.5c-23.5 6.3-42 24.9-48.3 48.6-11.4 42.9-11.4 132.3-11.4 132.3s0 89.4 11.4 132.3c6.3 23.7 24.8 41.5 48.3 47.8C117.2 448 288 448 288 448s170.8 0 213.4-11.5c23.5-6.3 42-24.2 48.3-47.8 11.4-42.9 11.4-132.3 11.4-132.3s0-89.4-11.4-132.3zm-317.5 213.5V175.2l142.7 81.2-142.7 81.2z\"\/>\r\n                <\/svg>\r\n            <\/span>\r\n            Subscribe on YouTube\r\n        <\/a>\r\n    <\/div> the ratio of 1 : 2 but in opposite direction before impact. This means that the total momentum of the system is zero.<\/p>\n<p>After the collision, the velocities of the balls will be in the same direction, but the velocities of the two balls will be in the ratio of 1 : 2. The velocity of the heavier ball will be half the original velocity, and the velocity of the lighter ball will be the original velocity.<\/p>\n<p>The following is a more detailed explanation of each option:<\/p>\n<ul>\n<li>Option A: The original velocity in the same direction. This is not possible because the total momentum of the system is zero.<\/li>\n<li>Option B: Half the original velocity in the same direction. This is possible, but it is not the only possible outcome.<\/li>\n<li>Option C: Half the original velocity in the opposite direction. This is possible, and it is the only possible outcome if the coefficient of restitution is $\\frac{1}{2}$.<\/li>\n<li>Option D: Original velocity in the opposite direction. This is not possible because the total momentum of the system is zero.<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Join Our Telegram Channel Subscribe on YouTube<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[645],"tags":[],"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>The masses of two balls are in the ratio of 2 : 1 and their respective velocities are in the ratio of 1 : 2 but in opposite direction before impact. If the coefficient of restitution is $$\\frac{1}{2}$$, the velocities of separation of the balls will be equal to A. Original velocity in the same direction B. Half the original velocity in the same direction C. Half the original velocity in the opposite direction D. Original velocity in the opposite direction<\/title>\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\/the-masses-of-two-balls-are-in-the-ratio-of-2-1-and-their-respective-velocities-are-in-the-ratio-of-1-2-but-in-opposite-direction-before-impact-if-the-coefficient-of-restitution-is-frac12\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"The masses of two balls are in the ratio of 2 : 1 and their respective velocities are in the ratio of 1 : 2 but in opposite direction before impact. If the coefficient of restitution is $$\\frac{1}{2}$$, the velocities of separation of the balls will be equal to A. Original velocity in the same direction B. Half the original velocity in the same direction C. Half the original velocity in the opposite direction D. Original velocity in the opposite direction\" \/>\n<meta property=\"og:description\" content=\"Join Our Telegram Channel Subscribe on YouTube\" \/>\n<meta property=\"og:url\" content=\"https:\/\/exam.pscnotes.com\/mcq\/the-masses-of-two-balls-are-in-the-ratio-of-2-1-and-their-respective-velocities-are-in-the-ratio-of-1-2-but-in-opposite-direction-before-impact-if-the-coefficient-of-restitution-is-frac12\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ and Quiz for Exams\" \/>\n<meta property=\"article:published_time\" content=\"2024-04-15T02:33:07+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":"The masses of two balls are in the ratio of 2 : 1 and their respective velocities are in the ratio of 1 : 2 but in opposite direction before impact. If the coefficient of restitution is $$\\frac{1}{2}$$, the velocities of separation of the balls will be equal to A. Original velocity in the same direction B. Half the original velocity in the same direction C. Half the original velocity in the opposite direction D. Original velocity in the opposite direction","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\/the-masses-of-two-balls-are-in-the-ratio-of-2-1-and-their-respective-velocities-are-in-the-ratio-of-1-2-but-in-opposite-direction-before-impact-if-the-coefficient-of-restitution-is-frac12\/","og_locale":"en_US","og_type":"article","og_title":"The masses of two balls are in the ratio of 2 : 1 and their respective velocities are in the ratio of 1 : 2 but in opposite direction before impact. If the coefficient of restitution is $$\\frac{1}{2}$$, the velocities of separation of the balls will be equal to A. Original velocity in the same direction B. Half the original velocity in the same direction C. Half the original velocity in the opposite direction D. Original velocity in the opposite direction","og_description":"Join Our Telegram Channel Subscribe on YouTube","og_url":"https:\/\/exam.pscnotes.com\/mcq\/the-masses-of-two-balls-are-in-the-ratio-of-2-1-and-their-respective-velocities-are-in-the-ratio-of-1-2-but-in-opposite-direction-before-impact-if-the-coefficient-of-restitution-is-frac12\/","og_site_name":"MCQ and Quiz for Exams","article_published_time":"2024-04-15T02:33:07+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\/the-masses-of-two-balls-are-in-the-ratio-of-2-1-and-their-respective-velocities-are-in-the-ratio-of-1-2-but-in-opposite-direction-before-impact-if-the-coefficient-of-restitution-is-frac12\/","url":"https:\/\/exam.pscnotes.com\/mcq\/the-masses-of-two-balls-are-in-the-ratio-of-2-1-and-their-respective-velocities-are-in-the-ratio-of-1-2-but-in-opposite-direction-before-impact-if-the-coefficient-of-restitution-is-frac12\/","name":"The masses of two balls are in the ratio of 2 : 1 and their respective velocities are in the ratio of 1 : 2 but in opposite direction before impact. If the coefficient of restitution is $$\\frac{1}{2}$$, the velocities of separation of the balls will be equal to A. Original velocity in the same direction B. Half the original velocity in the same direction C. Half the original velocity in the opposite direction D. Original velocity in the opposite direction","isPartOf":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#website"},"datePublished":"2024-04-15T02:33:07+00:00","dateModified":"2024-04-15T02:33:07+00:00","author":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209"},"breadcrumb":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/the-masses-of-two-balls-are-in-the-ratio-of-2-1-and-their-respective-velocities-are-in-the-ratio-of-1-2-but-in-opposite-direction-before-impact-if-the-coefficient-of-restitution-is-frac12\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/exam.pscnotes.com\/mcq\/the-masses-of-two-balls-are-in-the-ratio-of-2-1-and-their-respective-velocities-are-in-the-ratio-of-1-2-but-in-opposite-direction-before-impact-if-the-coefficient-of-restitution-is-frac12\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/exam.pscnotes.com\/mcq\/the-masses-of-two-balls-are-in-the-ratio-of-2-1-and-their-respective-velocities-are-in-the-ratio-of-1-2-but-in-opposite-direction-before-impact-if-the-coefficient-of-restitution-is-frac12\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/exam.pscnotes.com\/mcq\/"},{"@type":"ListItem","position":2,"name":"mcq","item":"https:\/\/exam.pscnotes.com\/mcq\/category\/mcq\/"},{"@type":"ListItem","position":3,"name":"Civil engineering","item":"https:\/\/exam.pscnotes.com\/mcq\/category\/mcq\/civil-engineering\/"},{"@type":"ListItem","position":4,"name":"Applied mechanics and graphic statics","item":"https:\/\/exam.pscnotes.com\/mcq\/category\/mcq\/civil-engineering\/applied-mechanics-and-graphic-statics\/"},{"@type":"ListItem","position":5,"name":"The masses of two balls are in the ratio of 2 : 1 and their respective velocities are in the ratio of 1 : 2 but in opposite direction before impact. If the coefficient of restitution is $$\\frac{1}{2}$$, the velocities of separation of the balls will be equal to A. Original velocity in the same direction B. Half the original velocity in the same direction C. Half the original velocity in the opposite direction D. Original velocity in the opposite direction"}]},{"@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\/d97f17072bfa490596c8f78363955d55?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/d97f17072bfa490596c8f78363955d55?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\/6717"}],"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=6717"}],"version-history":[{"count":0,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts\/6717\/revisions"}],"wp:attachment":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/media?parent=6717"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/categories?post=6717"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/tags?post=6717"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}