{"id":6774,"date":"2024-04-15T02:33:58","date_gmt":"2024-04-15T02:33:58","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=6774"},"modified":"2024-04-15T02:33:58","modified_gmt":"2024-04-15T02:33:58","slug":"a-circular-disc-rotates-at-n-rpm-the-angular-velocity-of-a-circular-ring-of-same-mass-and-radius-as-the-disc-and-to-have-the-same-angular-momentum-is-a-n-rpm-b-fractextn2-rpm-c","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/a-circular-disc-rotates-at-n-rpm-the-angular-velocity-of-a-circular-ring-of-same-mass-and-radius-as-the-disc-and-to-have-the-same-angular-momentum-is-a-n-rpm-b-fractextn2-rpm-c\/","title":{"rendered":"A circular disc rotates at n rpm. The angular velocity of a circular ring of same mass and radius as the disc and to have the same angular momentum is A. n rpm B. $$\\frac{{\\text{n}}}{2}$$ rpm C. $$\\frac{{\\text{n}}}{4}$$ rpm D. 2n rpm"},"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_6a9e3af671262\">\r\n                                            <div class=\"option\" data-option-key=\"option1\" data-is-correct=\"true\">\r\n                    n rpm                <\/div>\r\n                                            <div class=\"option\" data-option-key=\"option2\" data-is-correct=\"false\">\r\n                    $$\frac{{\text{n}}}{2}$$ rpm                <\/div>\r\n                                            <div class=\"option\" data-option-key=\"option3\" data-is-correct=\"false\">\r\n                    $$\frac{{\text{n}}}{4}$$ rpm                <\/div>\r\n                                            <div class=\"option\" data-option-key=\"option4\" data-is-correct=\"false\">\r\n                    2n rpm                <\/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 $\\boxed{\\frac{{\\text{n}}}{2}}$ rpm.<\/p>\n<p>Angular momentum is the rotational equivalent of linear momentum. It is a vector quantity, and its magnitude is given by the formula:<\/p>\n<p>$$L = I\\omega$$<\/p>\n<p>where $I$ is the moment of inertia and $\\omega$ is the angular velocity.<\/p>\n<p>The moment of inertia of a circular disc is given by the formula:<\/p>\n<p>$$I = \\frac{1}{2}mr^2$$<\/p>\n<p>where $m$ is the mass of the disc and $r$ is its <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            <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> <\/span>\r\n            Subscribe on YouTube\r\n        <\/a>\r\n    <\/div> radius.<\/p>\n<p>The angular velocity of a circular disc is given by the formula:<\/p>\n<p>$$\\omega = \\frac{2\\pi}{T}$$<\/p>\n<p>where $T$ is the period of rotation.<\/p>\n<p>The angular momentum of a circular disc is therefore given by the formula:<\/p>\n<p>$$L = \\frac{1}{2}mr^2\\frac{2\\pi}{T} = \\pi mr^2$$<\/p>\n<p>The moment of inertia of a circular ring is given by the formula:<\/p>\n<p>$$I = mr^2$$<\/p>\n<p>The angular velocity of a circular ring is given by the formula:<\/p>\n<p>$$\\omega = \\frac{2\\pi}{T}$$<\/p>\n<p>The angular momentum of a circular ring is therefore given by the formula:<\/p>\n<p>$$L = mr^2\\frac{2\\pi}{T} = 2\\pi mr^2$$<\/p>\n<p>For the circular disc and the circular ring to have the same angular momentum, the mass and radius of the two objects must be the same. The angular velocity of the circular ring must therefore be half the angular velocity of the circular disc.<\/p>\n<p>Therefore, the angular velocity of the circular ring is $\\boxed{\\frac{{\\text{n}}}{2}}$ rpm.<\/p>\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>A circular disc rotates at n rpm. 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