{"id":6866,"date":"2024-04-15T02:35:20","date_gmt":"2024-04-15T02:35:20","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=6866"},"modified":"2024-04-15T02:35:20","modified_gmt":"2024-04-15T02:35:20","slug":"the-height-at-which-the-end-of-a-rope-of-length-l-should-be-tied-so-that-a-man-pulling-at-the-other-end-may-have-the-greatest-tendency-to-overturn-the-pillar-is-a-frac34l-b-frac1","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/the-height-at-which-the-end-of-a-rope-of-length-l-should-be-tied-so-that-a-man-pulling-at-the-other-end-may-have-the-greatest-tendency-to-overturn-the-pillar-is-a-frac34l-b-frac1\/","title":{"rendered":"The height at which the end of a rope of length $$l$$ should be tied so that a man pulling at the other end may have the greatest tendency to overturn the pillar, is A. $$\\frac{3}{4}l$$ B. $$\\frac{1}{2}l$$ C. $$\\frac{l}{{\\sqrt 2 }}$$ D. $$\\frac{2}{{\\sqrt 3 }}l$$"},"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_6ab2ea5606467\">\r\n                                            <div class=\"option\" data-option-key=\"option1\" data-is-correct=\"true\">\r\n                    $$\frac{3}{4}l$$                <\/div>\r\n                                            <div class=\"option\" data-option-key=\"option2\" data-is-correct=\"false\">\r\n                    $$\frac{1}{2}l$$                <\/div>\r\n                                            <div class=\"option\" data-option-key=\"option3\" data-is-correct=\"false\">\r\n                    $$\frac{l}{{sqrt 2 }}$$                <\/div>\r\n                                            <div class=\"option\" data-option-key=\"option4\" data-is-correct=\"false\">\r\n                    $$\frac{2}{{sqrt 3 }}l$$                <\/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 $\\boxed{\\frac{l}{{\\sqrt 2 }}}$.<\/p>\n<p>The tendency of the man to overturn the pillar is proportional to the torque he exerts. The torque is the product of the force he exerts and the distance from the point of application of the force to the pivot point. The force the man exerts is equal to his weight, which is $mg$, where $m$ is his mass and $g$ is the acceleration due to gravity. The distance from the point of application of the force to the pivot point is the length of the rope, $l$.<\/p>\n<p>The torque is maximized when the force is applied at a right angle to the rope. This is the case when the rope is tied at a height of $\\frac{l}{{\\sqrt 2 }}$.<\/p>\n<p>Option A is incorrect because it is not a right angle to the rope. Option B is incorrect because it is not the maximum torque. <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> Option C is incorrect because it is not a right angle to the rope. Option D is incorrect because it is not the maximum torque.<\/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>The height at which the end of a rope of length $$l$$ should be tied so that a man pulling at the other end may have the greatest tendency to overturn the pillar, is A. $$\\frac{3}{4}l$$ B. $$\\frac{1}{2}l$$ C. $$\\frac{l}{{\\sqrt 2 }}$$ D. $$\\frac{2}{{\\sqrt 3 }}l$$<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" 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