{"id":6900,"date":"2024-04-15T02:35:50","date_gmt":"2024-04-15T02:35:50","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=6900"},"modified":"2024-04-15T02:35:50","modified_gmt":"2024-04-15T02:35:50","slug":"two-balls-of-masses-3-kg-and-6-kg-are-moving-with-velocities-of-4-m-sec-and-1-m-sec-respectively-towards-each-other-along-the-line-of-their-centers-after-impact-the-3-kg-ball-comes-to-rest-this-can","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/two-balls-of-masses-3-kg-and-6-kg-are-moving-with-velocities-of-4-m-sec-and-1-m-sec-respectively-towards-each-other-along-the-line-of-their-centers-after-impact-the-3-kg-ball-comes-to-rest-this-can\/","title":{"rendered":"Two balls of masses 3 kg and 6 kg are moving with velocities of 4 m\/sec and 1 m\/sec respectively, towards each other along the line of their centers. After impact the 3 kg ball comes to rest. This can happen only if the coefficient of restitution between the balls is A. $$\\frac{2}{3}$$ B. $$\\frac{1}{5}$$ C. $$\\frac{3}{5}$$ D. $$\\frac{1}{3}$$"},"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_6a9740f62ed4e\">\r\n                                            <div class=\"option\" data-option-key=\"option1\" data-is-correct=\"true\">\r\n                    $$\frac{2}{3}$$                <\/div>\r\n                                            <div class=\"option\" data-option-key=\"option2\" data-is-correct=\"false\">\r\n                    $$\frac{1}{5}$$                <\/div>\r\n                                            <div class=\"option\" data-option-key=\"option3\" data-is-correct=\"false\">\r\n                    $$\frac{3}{5}$$                <\/div>\r\n                                            <div class=\"option\" data-option-key=\"option4\" data-is-correct=\"false\">\r\n                    $$\frac{1}{3}$$                <\/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 $\\boxed{\\frac{1}{3}}$.<\/p>\n<p>The coefficient of restitution is a measure of how much energy is lost in an elastic collision. It is defined as the ratio of the relative velocity of separation to the relative velocity of approach. In this case, the relative velocity of approach is $4 &#8211; 1 = 3$ m\/s, and the relative velocity of separation is $0 &#8211; v_2 = -v_2$. Therefore, the coefficient of restitution is $e = \\frac{-v_2}{3}$.<\/p>\n<p>In order for the 3 kg ball to come to rest, the 6 kg ball must have a velocity of at least 3 m\/s after the collision. This means <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                   <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>  <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> that the coefficient of restitution must be at least $\\frac{1}{3}$.<\/p>\n<p>Option A: $\\frac{2}{3}$. This is not possible, because the 6 kg ball would have to have a velocity of less than 1 m\/s after the collision, which is impossible.<\/p>\n<p>Option B: $\\frac{1}{5}$. This is not possible, because the 6 kg ball would have to have a velocity of less than 0.6 m\/s after the collision, which is also impossible.<\/p>\n<p>Option C: $\\frac{3}{5}$. This is not possible, because the 6 kg ball would have to have a velocity of less than 0.4 m\/s after the collision, which is still impossible.<\/p>\n<p>Option D: $\\frac{1}{3}$. This is possible, because the 6 kg ball could have a velocity of 3 m\/s after the collision.<\/p>\n<p>Therefore, the correct answer is $\\boxed{\\frac{1}{3}}$.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>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>Two balls of masses 3 kg and 6 kg are moving with velocities of 4 m\/sec and 1 m\/sec respectively, towards each other along the line of their centers. After impact the 3 kg ball comes to rest. This can happen only if the coefficient of restitution between the balls is A. $$\\frac{2}{3}$$ B. $$\\frac{1}{5}$$ C. $$\\frac{3}{5}$$ D. $$\\frac{1}{3}$$<\/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\/two-balls-of-masses-3-kg-and-6-kg-are-moving-with-velocities-of-4-m-sec-and-1-m-sec-respectively-towards-each-other-along-the-line-of-their-centers-after-impact-the-3-kg-ball-comes-to-rest-this-can\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Two balls of masses 3 kg and 6 kg are moving with velocities of 4 m\/sec and 1 m\/sec respectively, towards each other along the line of their centers. After impact the 3 kg ball comes to rest. 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After impact the 3 kg ball comes to rest. This can happen only if the coefficient of restitution between the balls is A. $$\\frac{2}{3}$$ B. $$\\frac{1}{5}$$ C. $$\\frac{3}{5}$$ D. $$\\frac{1}{3}$$","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\/two-balls-of-masses-3-kg-and-6-kg-are-moving-with-velocities-of-4-m-sec-and-1-m-sec-respectively-towards-each-other-along-the-line-of-their-centers-after-impact-the-3-kg-ball-comes-to-rest-this-can\/","og_locale":"en_US","og_type":"article","og_title":"Two balls of masses 3 kg and 6 kg are moving with velocities of 4 m\/sec and 1 m\/sec respectively, towards each other along the line of their centers. After impact the 3 kg ball comes to rest. 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