{"id":20216,"date":"2024-04-15T05:49:57","date_gmt":"2024-04-15T05:49:57","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=20216"},"modified":"2024-04-15T05:49:57","modified_gmt":"2024-04-15T05:49:57","slug":"a-parabolic-cable-is-held-between-two-supports-at-the-same-level-the-horizontal-span-between-the-supports-is-l-the-sag-at-the-mid-span-is-h-the-equation-of-the-parabola-is-texty-4text","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/a-parabolic-cable-is-held-between-two-supports-at-the-same-level-the-horizontal-span-between-the-supports-is-l-the-sag-at-the-mid-span-is-h-the-equation-of-the-parabola-is-texty-4text\/","title":{"rendered":"A parabolic cable is held between two supports at the same level. The horizontal span between the supports is L. The sag at the mid-span is h. The equation of the parabola is \\[{\\text{y}} = 4{\\text{h}}\\left( {\\frac{{{{\\text{x}}^2}}}{{{{\\text{L}}^2}}}} \\right)\\] , where x is the horizontal coordinate and y is the vertical coordinate with the origin at the centre of the cable. The expression for the total length of the cable is A. \\[\\int\\limits_0^{\\text{L}} {\\sqrt {1 + 64\\frac{{{{\\text{h}}^2}{{\\text{x}}^2}}}{{{{\\text{L}}^4}}}} } {\\text{dx}}\\] B. \\[2\\int\\limits_0^{\\frac{{\\text{L}}}{2}} {\\sqrt {1 + 64\\frac{{{{\\text{h}}^3}{{\\text{x}}^2}}}{{{{\\text{L}}^4}}}} } {\\text{dx}}\\] C. \\[\\int\\limits_0^{\\frac{{\\text{L}}}{2}} {\\sqrt {1 + 64\\frac{{{{\\text{h}}^2}{{\\text{x}}^2}}}{{{{\\text{L}}^4}}}} } {\\text{dx}}\\] D. \\[2\\int\\limits_0^{\\frac{{\\text{L}}}{2}} {\\sqrt {1 + 64\\frac{{{{\\text{h}}^2}{{\\text{x}}^2}}}{{{{\\text{L}}^4}}}} } {\\text{dx}}\\]"},"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_6a9a873425a63\">\r\n                                            <div class=\"option\" data-option-key=\"option1\" data-is-correct=\"false\">\r\n                    &#8221;[intlimits_0^{\text{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    &#8221; option2=&#8221;\\[2\\int\\limits_0^{\\frac{{\\text{L}}}{2}} {\\sqrt {1 + 64\\frac{{{{\\text{h}}^3}{{\\text{x}}^2}}}{{{{\\text{L}}^4}}}} } {\\text{dx}}\\]&#8221; option3=&#8221;\\[\\int\\limits_0^{\\frac{{\\text{L}}}{2}} {\\sqrt {1 + 64\\frac{{{{\\text{h}}^2}{{\\text{x}}^2}}}{{{{\\text{L}}^4}}}} } {\\text{dx}}\\]&#8221; option4=&#8221;\\[2\\int\\limits_0^{\\frac{{\\text{L}}}{2}} {\\sqrt {1 + 64\\frac{{{{\\text{h}}^2}{{\\text{x}}^2}}}{{{{\\text{L}}^4}}}} } {\\text{dx}}\\]&#8221; correct=&#8221;option3&#8243;]<!--more--><\/p>\n<p>The correct answer is $\\boxed{\\text{C. }\\int\\limits_0^{\\frac{{\\text{L}}}{2}} {\\sqrt <div class=\"youtube-subscribe-container\">\r\n        <a href=\"https:\/\/www.youtube.com\/channel\/UCNHT8lW-JmLC68rjBfZhdkg?sub_confirmation=1\" target=\"_blank\" class=\"youtube-subscribe-button\">\r\n            <span class=\"youtube-icon\">\r\n               <div class=\"telegram-channel-container\">\r\n        <a href=\"https:\/\/t.me\/pscnotes2025\" target=\"_blank\" class=\"telegram-channel-button\">\r\n            <span class=\"telegram-icon\">\r\n                <svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" viewBox=\"0 0 496 512\">\r\n                    <path fill=\"white\" d=\"M248,8C111,8,0,119,0,256s111,248,248,248s248-111,248-248S385,8,248,8z M362,177L320,367c-3,14-10,18-20,14l-56-41l-27,26 c-3,3-5,5-10,5l4-63L323,196c5-5-1-7-8-3l-98,62l-42-13c-9-3-10-9,2-14l162-63C351,160,365,164,362,177z\"\/>\r\n                <\/svg>\r\n            <\/span>\r\n            Join Our Telegram Channel\r\n        <\/a>\r\n    <\/div>  <svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" viewBox=\"0 0 576 512\">\r\n                    <path d=\"M549.7 124.1c-6.3-23.7-24.8-42.3-48.3-48.6C458.8 64 288 64 288 64S117.2 64 74.6 75.5c-23.5 6.3-42 24.9-48.3 48.6-11.4 42.9-11.4 132.3-11.4 132.3s0 89.4 11.4 132.3c6.3 23.7 24.8 41.5 48.3 47.8C117.2 448 288 448 288 448s170.8 0 213.4-11.5c23.5-6.3 42-24.2 48.3-47.8 11.4-42.9 11.4-132.3 11.4-132.3s0-89.4-11.4-132.3zm-317.5 213.5V175.2l142.7 81.2-142.7 81.2z\"\/>\r\n                <\/svg>\r\n            <\/span>\r\n            Subscribe on YouTube\r\n        <\/a>\r\n    <\/div> {1 + 64\\frac{{{{\\text{h}}^2}{{\\text{x}}^2}}}{{{{\\text{L}}^4}}}} } {\\text{dx}}}$.<\/p>\n<p>The total length of the cable is the sum of the lengths of the two legs of the parabola. The length of each leg is equal to the arc length of the parabola from the origin to the point where it intersects the x-axis. The arc length of a parabola is given by the following formula:<\/p>\n<p>$$L = \\int_0^a \\sqrt{1 + \\left(\\frac{dy}{dx}\\right)^2} dx$$<\/p>\n<p>In this case, the derivative of the equation of the parabola is $dy\/dx = 8h x\/L^2$. Substituting this into the formula for the arc length, we get:<\/p>\n<p>$$L = \\int_0^a \\sqrt{1 + \\left(\\frac{8h x}{L^2}\\right)^2} dx = \\int_0^a \\sqrt{1 + 64\\frac{{{{\\text{h}}^2}{{\\text{x}}^2}}}{{{{\\text{L}}^4}}}} } {\\text{dx}}$$<\/p>\n<p>The integral is evaluated from $x=0$ to $x=L\/2$, since the parabola intersects the x-axis at $x=L\/2$. Therefore, the total length of the cable is:<\/p>\n<p>$$L = 2 \\int_0^{\\frac{{\\text{L}}}{2}} {\\sqrt {1 + 64\\frac{{{{\\text{h}}^2}{{\\text{x}}^2}}}{{{{\\text{L}}^4}}}} } {\\text{dx}}$$<\/p>\n","protected":false},"excerpt":{"rendered":"<p>&#8221; option2=&#8221;\\[2\\int\\limits_0^{\\frac{{\\text{L}}}{2}} {\\sqrt {1 + 64\\frac{{{{\\text{h}}^3}{{\\text{x}}^2}}}{{{{\\text{L}}^4}}}} } {\\text{dx}}\\]&#8221; option3=&#8221;\\[\\int\\limits_0^{\\frac{{\\text{L}}}{2}} {\\sqrt {1 + 64\\frac{{{{\\text{h}}^2}{{\\text{x}}^2}}}{{{{\\text{L}}^4}}}} } {\\text{dx}}\\]&#8221; option4=&#8221;\\[2\\int\\limits_0^{\\frac{{\\text{L}}}{2}} {\\sqrt Join Our Telegram Channel Subscribe on YouTube {1 + 64\\frac{{{{\\text{h}}^2}{{\\text{x}}^2}}}{{{{\\text{L}}^4}}}} } {\\text{dx}}\\]&#8221; correct=&#8221;option3&#8243;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[690],"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 parabolic cable is held between two supports at the same level. The horizontal span between the supports is L. The sag at the mid-span is h. The equation of the parabola is \\[{\\text{y}} = 4{\\text{h}}\\left( {\\frac{{{{\\text{x}}^2}}}{{{{\\text{L}}^2}}}} \\right)\\] , where x is the horizontal coordinate and y is the vertical coordinate with the origin at the centre of the cable. The expression for the total length of the cable is A. \\[\\int\\limits_0^{\\text{L}} {\\sqrt {1 + 64\\frac{{{{\\text{h}}^2}{{\\text{x}}^2}}}{{{{\\text{L}}^4}}}} } {\\text{dx}}\\] B. \\[2\\int\\limits_0^{\\frac{{\\text{L}}}{2}} {\\sqrt {1 + 64\\frac{{{{\\text{h}}^3}{{\\text{x}}^2}}}{{{{\\text{L}}^4}}}} } {\\text{dx}}\\] C. \\[\\int\\limits_0^{\\frac{{\\text{L}}}{2}} {\\sqrt {1 + 64\\frac{{{{\\text{h}}^2}{{\\text{x}}^2}}}{{{{\\text{L}}^4}}}} } {\\text{dx}}\\] D. \\[2\\int\\limits_0^{\\frac{{\\text{L}}}{2}} {\\sqrt {1 + 64\\frac{{{{\\text{h}}^2}{{\\text{x}}^2}}}{{{{\\text{L}}^4}}}} } {\\text{dx}}\\]<\/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\/a-parabolic-cable-is-held-between-two-supports-at-the-same-level-the-horizontal-span-between-the-supports-is-l-the-sag-at-the-mid-span-is-h-the-equation-of-the-parabola-is-texty-4text\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"A parabolic cable is held between two supports at the same level. The horizontal span between the supports is L. The sag at the mid-span is h. The equation of the parabola is \\[{\\text{y}} = 4{\\text{h}}\\left( {\\frac{{{{\\text{x}}^2}}}{{{{\\text{L}}^2}}}} \\right)\\] , where x is the horizontal coordinate and y is the vertical coordinate with the origin at the centre of the cable. The expression for the total length of the cable is A. \\[\\int\\limits_0^{\\text{L}} {\\sqrt {1 + 64\\frac{{{{\\text{h}}^2}{{\\text{x}}^2}}}{{{{\\text{L}}^4}}}} } {\\text{dx}}\\] B. \\[2\\int\\limits_0^{\\frac{{\\text{L}}}{2}} {\\sqrt {1 + 64\\frac{{{{\\text{h}}^3}{{\\text{x}}^2}}}{{{{\\text{L}}^4}}}} } {\\text{dx}}\\] C. \\[\\int\\limits_0^{\\frac{{\\text{L}}}{2}} {\\sqrt {1 + 64\\frac{{{{\\text{h}}^2}{{\\text{x}}^2}}}{{{{\\text{L}}^4}}}} } {\\text{dx}}\\] D. \\[2\\int\\limits_0^{\\frac{{\\text{L}}}{2}} {\\sqrt {1 + 64\\frac{{{{\\text{h}}^2}{{\\text{x}}^2}}}{{{{\\text{L}}^4}}}} } {\\text{dx}}\\]\" \/>\n<meta property=\"og:description\" content=\"&#8221; option2=&#8221;[2intlimits_0^{frac{{text{L}}}{2}} {sqrt {1 + 64frac{{{{text{h}}^3}{{text{x}}^2}}}{{{{text{L}}^4}}}} } {text{dx}}]&#8221; option3=&#8221;[intlimits_0^{frac{{text{L}}}{2}} {sqrt {1 + 64frac{{{{text{h}}^2}{{text{x}}^2}}}{{{{text{L}}^4}}}} } {text{dx}}]&#8221; Join Our Telegram Channel Subscribe on YouTube option4=&#8221;[2intlimits_0^{frac{{text{L}}}{2}} {sqrt {1 + 64frac{{{{text{h}}^2}{{text{x}}^2}}}{{{{text{L}}^4}}}} } {text{dx}}]&#8221; correct=&#8221;option3&#8243;]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/exam.pscnotes.com\/mcq\/a-parabolic-cable-is-held-between-two-supports-at-the-same-level-the-horizontal-span-between-the-supports-is-l-the-sag-at-the-mid-span-is-h-the-equation-of-the-parabola-is-texty-4text\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ and Quiz for Exams\" \/>\n<meta property=\"article:published_time\" content=\"2024-04-15T05:49:57+00:00\" \/>\n<meta name=\"author\" content=\"rawan239\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"rawan239\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 minute\" \/>\n<!-- \/ Yoast SEO Premium plugin. -->","yoast_head_json":{"title":"A parabolic cable is held between two supports at the same level. The horizontal span between the supports is L. The sag at the mid-span is h. The equation of the parabola is \\[{\\text{y}} = 4{\\text{h}}\\left( {\\frac{{{{\\text{x}}^2}}}{{{{\\text{L}}^2}}}} \\right)\\] , where x is the horizontal coordinate and y is the vertical coordinate with the origin at the centre of the cable. The expression for the total length of the cable is A. \\[\\int\\limits_0^{\\text{L}} {\\sqrt {1 + 64\\frac{{{{\\text{h}}^2}{{\\text{x}}^2}}}{{{{\\text{L}}^4}}}} } {\\text{dx}}\\] B. \\[2\\int\\limits_0^{\\frac{{\\text{L}}}{2}} {\\sqrt {1 + 64\\frac{{{{\\text{h}}^3}{{\\text{x}}^2}}}{{{{\\text{L}}^4}}}} } {\\text{dx}}\\] C. \\[\\int\\limits_0^{\\frac{{\\text{L}}}{2}} {\\sqrt {1 + 64\\frac{{{{\\text{h}}^2}{{\\text{x}}^2}}}{{{{\\text{L}}^4}}}} } {\\text{dx}}\\] D. \\[2\\int\\limits_0^{\\frac{{\\text{L}}}{2}} {\\sqrt {1 + 64\\frac{{{{\\text{h}}^2}{{\\text{x}}^2}}}{{{{\\text{L}}^4}}}} } {\\text{dx}}\\]","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\/a-parabolic-cable-is-held-between-two-supports-at-the-same-level-the-horizontal-span-between-the-supports-is-l-the-sag-at-the-mid-span-is-h-the-equation-of-the-parabola-is-texty-4text\/","og_locale":"en_US","og_type":"article","og_title":"A parabolic cable is held between two supports at the same level. The horizontal span between the supports is L. The sag at the mid-span is h. The equation of the parabola is \\[{\\text{y}} = 4{\\text{h}}\\left( {\\frac{{{{\\text{x}}^2}}}{{{{\\text{L}}^2}}}} \\right)\\] , where x is the horizontal coordinate and y is the vertical coordinate with the origin at the centre of the cable. The expression for the total length of the cable is A. \\[\\int\\limits_0^{\\text{L}} {\\sqrt {1 + 64\\frac{{{{\\text{h}}^2}{{\\text{x}}^2}}}{{{{\\text{L}}^4}}}} } {\\text{dx}}\\] B. \\[2\\int\\limits_0^{\\frac{{\\text{L}}}{2}} {\\sqrt {1 + 64\\frac{{{{\\text{h}}^3}{{\\text{x}}^2}}}{{{{\\text{L}}^4}}}} } {\\text{dx}}\\] C. \\[\\int\\limits_0^{\\frac{{\\text{L}}}{2}} {\\sqrt {1 + 64\\frac{{{{\\text{h}}^2}{{\\text{x}}^2}}}{{{{\\text{L}}^4}}}} } {\\text{dx}}\\] D. \\[2\\int\\limits_0^{\\frac{{\\text{L}}}{2}} {\\sqrt {1 + 64\\frac{{{{\\text{h}}^2}{{\\text{x}}^2}}}{{{{\\text{L}}^4}}}} } {\\text{dx}}\\]","og_description":"&#8221; option2=&#8221;[2intlimits_0^{frac{{text{L}}}{2}} {sqrt {1 + 64frac{{{{text{h}}^3}{{text{x}}^2}}}{{{{text{L}}^4}}}} } {text{dx}}]&#8221; option3=&#8221;[intlimits_0^{frac{{text{L}}}{2}} {sqrt {1 + 64frac{{{{text{h}}^2}{{text{x}}^2}}}{{{{text{L}}^4}}}} } {text{dx}}]&#8221; Join Our Telegram Channel Subscribe on YouTube option4=&#8221;[2intlimits_0^{frac{{text{L}}}{2}} {sqrt {1 + 64frac{{{{text{h}}^2}{{text{x}}^2}}}{{{{text{L}}^4}}}} } {text{dx}}]&#8221; correct=&#8221;option3&#8243;]","og_url":"https:\/\/exam.pscnotes.com\/mcq\/a-parabolic-cable-is-held-between-two-supports-at-the-same-level-the-horizontal-span-between-the-supports-is-l-the-sag-at-the-mid-span-is-h-the-equation-of-the-parabola-is-texty-4text\/","og_site_name":"MCQ and Quiz for Exams","article_published_time":"2024-04-15T05:49:57+00:00","author":"rawan239","twitter_card":"summary_large_image","twitter_misc":{"Written by":"rawan239","Est. reading time":"1 minute"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/exam.pscnotes.com\/mcq\/a-parabolic-cable-is-held-between-two-supports-at-the-same-level-the-horizontal-span-between-the-supports-is-l-the-sag-at-the-mid-span-is-h-the-equation-of-the-parabola-is-texty-4text\/","url":"https:\/\/exam.pscnotes.com\/mcq\/a-parabolic-cable-is-held-between-two-supports-at-the-same-level-the-horizontal-span-between-the-supports-is-l-the-sag-at-the-mid-span-is-h-the-equation-of-the-parabola-is-texty-4text\/","name":"A parabolic cable is held between two supports at the same level. The horizontal span between the supports is L. The sag at the mid-span is h. The equation of the parabola is \\[{\\text{y}} = 4{\\text{h}}\\left( {\\frac{{{{\\text{x}}^2}}}{{{{\\text{L}}^2}}}} \\right)\\] , where x is the horizontal coordinate and y is the vertical coordinate with the origin at the centre of the cable. The expression for the total length of the cable is A. \\[\\int\\limits_0^{\\text{L}} {\\sqrt {1 + 64\\frac{{{{\\text{h}}^2}{{\\text{x}}^2}}}{{{{\\text{L}}^4}}}} } {\\text{dx}}\\] B. \\[2\\int\\limits_0^{\\frac{{\\text{L}}}{2}} {\\sqrt {1 + 64\\frac{{{{\\text{h}}^3}{{\\text{x}}^2}}}{{{{\\text{L}}^4}}}} } {\\text{dx}}\\] C. \\[\\int\\limits_0^{\\frac{{\\text{L}}}{2}} {\\sqrt {1 + 64\\frac{{{{\\text{h}}^2}{{\\text{x}}^2}}}{{{{\\text{L}}^4}}}} } {\\text{dx}}\\] D. \\[2\\int\\limits_0^{\\frac{{\\text{L}}}{2}} {\\sqrt {1 + 64\\frac{{{{\\text{h}}^2}{{\\text{x}}^2}}}{{{{\\text{L}}^4}}}} } {\\text{dx}}\\]","isPartOf":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#website"},"datePublished":"2024-04-15T05:49:57+00:00","dateModified":"2024-04-15T05:49:57+00:00","author":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209"},"breadcrumb":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/a-parabolic-cable-is-held-between-two-supports-at-the-same-level-the-horizontal-span-between-the-supports-is-l-the-sag-at-the-mid-span-is-h-the-equation-of-the-parabola-is-texty-4text\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/exam.pscnotes.com\/mcq\/a-parabolic-cable-is-held-between-two-supports-at-the-same-level-the-horizontal-span-between-the-supports-is-l-the-sag-at-the-mid-span-is-h-the-equation-of-the-parabola-is-texty-4text\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/exam.pscnotes.com\/mcq\/a-parabolic-cable-is-held-between-two-supports-at-the-same-level-the-horizontal-span-between-the-supports-is-l-the-sag-at-the-mid-span-is-h-the-equation-of-the-parabola-is-texty-4text\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/exam.pscnotes.com\/mcq\/"},{"@type":"ListItem","position":2,"name":"mcq","item":"https:\/\/exam.pscnotes.com\/mcq\/category\/mcq\/"},{"@type":"ListItem","position":3,"name":"Engineering maths","item":"https:\/\/exam.pscnotes.com\/mcq\/category\/mcq\/engineering-maths\/"},{"@type":"ListItem","position":4,"name":"Calculus","item":"https:\/\/exam.pscnotes.com\/mcq\/category\/mcq\/engineering-maths\/calculus\/"},{"@type":"ListItem","position":5,"name":"A parabolic cable is held between two supports at the same level. The horizontal span between the supports is L. The sag at the mid-span is h. The equation of the parabola is \\[{\\text{y}} = 4{\\text{h}}\\left( {\\frac{{{{\\text{x}}^2}}}{{{{\\text{L}}^2}}}} \\right)\\] , where x is the horizontal coordinate and y is the vertical coordinate with the origin at the centre of the cable. The expression for the total length of the cable is A. \\[\\int\\limits_0^{\\text{L}} {\\sqrt {1 + 64\\frac{{{{\\text{h}}^2}{{\\text{x}}^2}}}{{{{\\text{L}}^4}}}} } {\\text{dx}}\\] B. \\[2\\int\\limits_0^{\\frac{{\\text{L}}}{2}} {\\sqrt {1 + 64\\frac{{{{\\text{h}}^3}{{\\text{x}}^2}}}{{{{\\text{L}}^4}}}} } {\\text{dx}}\\] C. \\[\\int\\limits_0^{\\frac{{\\text{L}}}{2}} {\\sqrt {1 + 64\\frac{{{{\\text{h}}^2}{{\\text{x}}^2}}}{{{{\\text{L}}^4}}}} } {\\text{dx}}\\] D. \\[2\\int\\limits_0^{\\frac{{\\text{L}}}{2}} {\\sqrt {1 + 64\\frac{{{{\\text{h}}^2}{{\\text{x}}^2}}}{{{{\\text{L}}^4}}}} } {\\text{dx}}\\]"}]},{"@type":"WebSite","@id":"https:\/\/exam.pscnotes.com\/mcq\/#website","url":"https:\/\/exam.pscnotes.com\/mcq\/","name":"MCQ and Quiz for Exams","description":"","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/exam.pscnotes.com\/mcq\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"en-US"},{"@type":"Person","@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209","name":"rawan239","image":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/image\/","url":"https:\/\/secure.gravatar.com\/avatar\/d97f17072bfa490596c8f78363955d55?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/d97f17072bfa490596c8f78363955d55?s=96&d=mm&r=g","caption":"rawan239"},"sameAs":["https:\/\/exam.pscnotes.com"],"url":"https:\/\/exam.pscnotes.com\/mcq\/author\/rawan239\/"}]}},"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts\/20216"}],"collection":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/comments?post=20216"}],"version-history":[{"count":0,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts\/20216\/revisions"}],"wp:attachment":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/media?parent=20216"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/categories?post=20216"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/tags?post=20216"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}