{"id":5640,"date":"2024-04-15T02:16:34","date_gmt":"2024-04-15T02:16:34","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=5640"},"modified":"2024-04-15T02:16:34","modified_gmt":"2024-04-15T02:16:34","slug":"textp-frac4pi-2texteitextl2-is-the-equation-of-eulers-crippling-load-if-a-both-the-ends-are-fixed-b-both-the-ends-are-hinged-c-one-end-is-fixed-and-other","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/textp-frac4pi-2texteitextl2-is-the-equation-of-eulers-crippling-load-if-a-both-the-ends-are-fixed-b-both-the-ends-are-hinged-c-one-end-is-fixed-and-other\/","title":{"rendered":"$${\\text{P}} = \\frac{{4{\\pi ^2}{\\text{E}}I}}{{{{\\text{L}}^2}}}$$ is the equation of Euler&#8217;s crippling load if A. Both the ends are fixed B. Both the ends are hinged C. One end is fixed and other end is free D. One end is fixed and other end is hinged"},"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_6a99907771b31\">\r\n                                            <div class=\"option\" data-option-key=\"option1\" data-is-correct=\"false\">\r\n                    Both the ends are fixed                <\/div>\r\n                                            <div class=\"option\" data-option-key=\"option2\" data-is-correct=\"false\">\r\n                    Both the ends are hinged                <\/div>\r\n                                            <div class=\"option\" data-option-key=\"option3\" data-is-correct=\"true\">\r\n                    One end is fixed and other end is free                <\/div>\r\n                                            <div class=\"option\" data-option-key=\"option4\" data-is-correct=\"false\">\r\n                    One end is fixed and other end is hinged                <\/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: <strong>C. One end is fixed and other end is free.<\/strong><\/p>\n<p>Euler&#8217;s crippling load is the maximum load that a column can support without buckling. The equation for Euler&#8217;s crippling load is:<\/p>\n<p>$$P = \\frac{{4{\\pi ^2}{\\text{E}}I}}{{{{\\text{L}}^2}}}$$<\/p>\n<p>where:<\/p>\n<ul>\n<li>$P$ is the Euler&#8217;s crippling load<\/li>\n<li>$E$ is the Young&#8217;s modulus of the material<\/li>\n<li>$I$ is the moment of inertia of the cross-section of the column<\/li>\n<li>$L$ <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  <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>           Subscribe on YouTube\r\n        <\/a>\r\n    <\/div> is the length of the column<\/li>\n<\/ul>\n<p>For a column with one end fixed and the other end free, the moment of inertia is given by:<\/p>\n<p>$$I = \\frac{1}{3}bh^3$$<\/p>\n<p>where:<\/p>\n<ul>\n<li>$b$ is the width of the column<\/li>\n<li>$h$ is the height of the column<\/li>\n<\/ul>\n<p>Substituting this into the equation for Euler&#8217;s crippling load gives:<\/p>\n<p>$$P = \\frac{{4{\\pi ^2}{\\text{E}} \\left( \\frac{1}{3}bh^3 \\right)}}{{{{\\text{L}}^2}}}$$<\/p>\n<p>$$P = \\frac{{16{\\pi ^2}{\\text{E}}bh^2}}{{9{{\\text{L}}^2}}}$$<\/p>\n<p>Therefore, the equation for Euler&#8217;s crippling load for a column with one end fixed and the other end free is:<\/p>\n<p>$$P = \\frac{{16{\\pi ^2}{\\text{E}}bh^2}}{{9{{\\text{L}}^2}}}$$<\/p>\n<p>The other options are incorrect because they do not give the correct equation for Euler&#8217;s crippling load for a column with one end fixed and the other end free.<\/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":[639],"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>$${\\text{P}} = \\frac{{4{\\pi ^2}{\\text{E}}I}}{{{{\\text{L}}^2}}}$$ is the equation of Euler&#039;s crippling load if A. 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