{"id":6778,"date":"2024-04-15T02:34:02","date_gmt":"2024-04-15T02:34:02","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=6778"},"modified":"2024-04-15T02:34:02","modified_gmt":"2024-04-15T02:34:02","slug":"a-simple-pendulum-of-length-l-has-an-energy-e-when-its-amplitude-is-a-if-its-amplitude-is-increased-to-2a-the-energy-becomes-a-e-b-fractexte2-c-2e-d-4e","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/a-simple-pendulum-of-length-l-has-an-energy-e-when-its-amplitude-is-a-if-its-amplitude-is-increased-to-2a-the-energy-becomes-a-e-b-fractexte2-c-2e-d-4e\/","title":{"rendered":"A simple pendulum of length L has an energy E when its amplitude is A. If its amplitude is increased to 2A, the energy becomes A. E B. $$\\frac{{\\text{E}}}{2}$$ C. 2E D. 4E"},"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_6a9e7e641d6c7\">\r\n                                            <div class=\"option\" data-option-key=\"option1\" data-is-correct=\"false\">\r\n                    If its amplitude is increased to 2A, the energy becomes A. E                <\/div>\r\n                                            <div class=\"option\" data-option-key=\"option2\" data-is-correct=\"false\">\r\n                    $$\frac{{\text{E}}}{2}$$                <\/div>\r\n                                            <div class=\"option\" data-option-key=\"option3\" data-is-correct=\"true\">\r\n                    2E                <\/div>\r\n                                            <div class=\"option\" data-option-key=\"option4\" data-is-correct=\"false\">\r\n                    4E                <\/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 C. 2E.<\/p>\n<p>The energy of a simple pendulum is given by the equation:<\/p>\n<p>$$E = \\frac{1}{2}m\\omega^2L^2$$<\/p>\n<p>where $m$ is the mass of the pendulum, $\\omega$ is the angular frequency, and $L$ is the length of the pendulum.<\/p>\n<p>The angular frequency is given by the equation:<\/p>\n<p>$$\\omega = \\sqrt{\\frac{g}{L}}$$<\/p>\n<p>where $g$ is the acceleration due to gravity.<\/p>\n<p>When the amplitude is increased to 2A, the length of the pendulum does not change, so the angular frequency does not change. However, the energy of the pendulum is proportional to the square of the angular frequency, so the energy of the pendulum <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> increases to 2E.<\/p>\n<p>Option A is incorrect because the energy of the pendulum <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> does not change when the amplitude is increased.<\/p>\n<p>Option B is incorrect because the energy of the pendulum is proportional to the square of the angular frequency, so the energy of the pendulum increases to 2E when the amplitude is increased to 2A.<\/p>\n<p>Option D is incorrect because the energy of the pendulum is proportional to the square of the angular frequency, so the energy of the pendulum increases to 4E when the amplitude is increased to 4A.<\/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 simple pendulum of length L has an energy E when its amplitude is A. 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