{"id":6173,"date":"2024-04-15T02:24:57","date_gmt":"2024-04-15T02:24:57","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=6173"},"modified":"2024-04-15T02:24:57","modified_gmt":"2024-04-15T02:24:57","slug":"according-to-rankines-formula-minimum-depth-of-foundations-is-a-fractextptextw-times-left-frac1-sin-varphi-1-sin-varphi-right2-b-fra","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/according-to-rankines-formula-minimum-depth-of-foundations-is-a-fractextptextw-times-left-frac1-sin-varphi-1-sin-varphi-right2-b-fra\/","title":{"rendered":"According to Rankine&#8217;s formula, minimum depth of foundations, is A. $$\\frac{{\\text{P}}}{{\\text{w}}} \\times {\\left( {\\frac{{1 + \\sin \\varphi }}{{1 &#8211; \\sin \\varphi }}} \\right)^2}$$ B. $$\\frac{{\\text{P}}}{{\\text{w}}} \\times {\\left( {\\frac{{1 &#8211; \\sin \\varphi }}{{1 + \\sin \\varphi }}} \\right)^2}$$ C. $$\\frac{{\\text{P}}}{{2{\\text{w}}}} \\times {\\left( {\\frac{{1 &#8211; \\sin \\varphi }}{{1 + \\sin \\varphi }}} \\right)^2}$$ D. $$\\frac{{\\text{P}}}{{\\text{w}}} \\times \\frac{{1 + \\sin \\varphi }}{{1 &#8211; \\sin \\varphi }}$$"},"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_6a9d9ea3d425e\">\r\n                                            <div class=\"option\" data-option-key=\"option1\" data-is-correct=\"false\">\r\n                    $$\frac{{\text{P}}}{{\text{w}}} \times {left( {\frac{{1 + sin \u000barphi }}{{1 - sin \u000barphi }}} \right)^2}$$                <\/div>\r\n                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            <div class=\"option\" data-option-key=\"option3\" data-is-correct=\"true\">\r\n                    $$\frac{{\text{P}}}{{2{\text{w}}}} \times {left( {\frac{{1 - sin \u000barphi }}{{1 + sin \u000barphi }}} \right)^2}$$                <\/div>\r\n                                            <div class=\"option\" data-option-key=\"option4\" data-is-correct=\"false\">\r\n                    $$\frac{{\text{P}}}{{\text{w}}} \times \frac{{1 + sin \u000barphi }}{{1 - sin \u000barphi }}$$                <\/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 $\\boxed{\\frac{{\\text{P}}}{{\\text{w}}} \\times {\\left( {\\frac{{1 &#8211; \\sin \\varphi }}{{1 + \\sin \\varphi }}} \\right)^2}}$.<\/p>\n<p>Rankine&#8217;s formula is used to calculate the minimum depth of foundations for retaining walls. The formula is given by:<\/p>\n<p>$$d = \\frac{{\\text{P}}}{{\\text{w}}} \\times {\\left( {\\frac{{1 &#8211; \\sin \\varphi }}{{1 + \\sin \\varphi }}} \\right)^2}$$<\/p>\n<p>where:<\/p>\n<ul>\n<li>$d$ is the minimum depth of foundation<\/li>\n<li>$P$ is the active earth pressure<\/li>\n<li>$w$ is the weight of the soil above the foundation<\/li>\n<li>$\\varphi$ is the angle of internal friction of the soil<\/li>\n<\/ul>\n<p>The formula takes into account the weight of the soil above the foundation, the active earth pressure, and the angle of internal friction of the soil. The minimum depth of foundation is calculated by dividing the active earth pressure by the weight of the soil above the foundation and multiplying by the square of the tangent of the angle of internal friction of the soil.<\/p>\n<p>The other options are incorrect because they do not take into account the weight of the soil above the foundation.<\/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":[643],"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>According to Rankine&#039;s formula, minimum depth of foundations, is A. $$\\frac{{\\text{P}}}{{\\text{w}}} \\times {\\left( {\\frac{{1 + \\sin \\varphi }}{{1 - \\sin \\varphi }}} \\right)^2}$$ B. $$\\frac{{\\text{P}}}{{\\text{w}}} \\times {\\left( {\\frac{{1 - \\sin \\varphi }}{{1 + \\sin \\varphi }}} \\right)^2}$$ C. $$\\frac{{\\text{P}}}{{2{\\text{w}}}} \\times {\\left( {\\frac{{1 - \\sin \\varphi }}{{1 + \\sin \\varphi }}} \\right)^2}$$ D. $$\\frac{{\\text{P}}}{{\\text{w}}} \\times \\frac{{1 + \\sin \\varphi }}{{1 - \\sin \\varphi }}$$<\/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\/according-to-rankines-formula-minimum-depth-of-foundations-is-a-fractextptextw-times-left-frac1-sin-varphi-1-sin-varphi-right2-b-fra\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"According to Rankine&#039;s formula, minimum depth of foundations, is A. $$\\frac{{\\text{P}}}{{\\text{w}}} \\times {\\left( {\\frac{{1 + \\sin \\varphi }}{{1 - \\sin \\varphi }}} \\right)^2}$$ B. $$\\frac{{\\text{P}}}{{\\text{w}}} \\times {\\left( {\\frac{{1 - \\sin \\varphi }}{{1 + \\sin \\varphi }}} \\right)^2}$$ C. $$\\frac{{\\text{P}}}{{2{\\text{w}}}} \\times {\\left( {\\frac{{1 - \\sin \\varphi }}{{1 + \\sin \\varphi }}} \\right)^2}$$ D. $$\\frac{{\\text{P}}}{{\\text{w}}} \\times \\frac{{1 + \\sin \\varphi }}{{1 - \\sin \\varphi }}$$\" \/>\n<meta property=\"og:description\" content=\"Join Our Telegram Channel Subscribe on YouTube\" \/>\n<meta property=\"og:url\" content=\"https:\/\/exam.pscnotes.com\/mcq\/according-to-rankines-formula-minimum-depth-of-foundations-is-a-fractextptextw-times-left-frac1-sin-varphi-1-sin-varphi-right2-b-fra\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ and Quiz for Exams\" \/>\n<meta property=\"article:published_time\" content=\"2024-04-15T02:24:57+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":"According to Rankine's formula, minimum depth of foundations, is A. $$\\frac{{\\text{P}}}{{\\text{w}}} \\times {\\left( {\\frac{{1 + \\sin \\varphi }}{{1 - \\sin \\varphi }}} \\right)^2}$$ B. $$\\frac{{\\text{P}}}{{\\text{w}}} \\times {\\left( {\\frac{{1 - \\sin \\varphi }}{{1 + \\sin \\varphi }}} \\right)^2}$$ C. $$\\frac{{\\text{P}}}{{2{\\text{w}}}} \\times {\\left( {\\frac{{1 - \\sin \\varphi }}{{1 + \\sin \\varphi }}} \\right)^2}$$ D. $$\\frac{{\\text{P}}}{{\\text{w}}} \\times \\frac{{1 + \\sin \\varphi }}{{1 - \\sin \\varphi }}$$","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\/according-to-rankines-formula-minimum-depth-of-foundations-is-a-fractextptextw-times-left-frac1-sin-varphi-1-sin-varphi-right2-b-fra\/","og_locale":"en_US","og_type":"article","og_title":"According to Rankine's formula, minimum depth of foundations, is A. $$\\frac{{\\text{P}}}{{\\text{w}}} \\times {\\left( {\\frac{{1 + \\sin \\varphi }}{{1 - \\sin \\varphi }}} \\right)^2}$$ B. $$\\frac{{\\text{P}}}{{\\text{w}}} \\times {\\left( {\\frac{{1 - \\sin \\varphi }}{{1 + \\sin \\varphi }}} \\right)^2}$$ C. $$\\frac{{\\text{P}}}{{2{\\text{w}}}} \\times {\\left( {\\frac{{1 - \\sin \\varphi }}{{1 + \\sin \\varphi }}} \\right)^2}$$ D. $$\\frac{{\\text{P}}}{{\\text{w}}} \\times \\frac{{1 + \\sin \\varphi }}{{1 - \\sin \\varphi }}$$","og_description":"Join Our Telegram Channel Subscribe on YouTube","og_url":"https:\/\/exam.pscnotes.com\/mcq\/according-to-rankines-formula-minimum-depth-of-foundations-is-a-fractextptextw-times-left-frac1-sin-varphi-1-sin-varphi-right2-b-fra\/","og_site_name":"MCQ and Quiz for Exams","article_published_time":"2024-04-15T02:24:57+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\/according-to-rankines-formula-minimum-depth-of-foundations-is-a-fractextptextw-times-left-frac1-sin-varphi-1-sin-varphi-right2-b-fra\/","url":"https:\/\/exam.pscnotes.com\/mcq\/according-to-rankines-formula-minimum-depth-of-foundations-is-a-fractextptextw-times-left-frac1-sin-varphi-1-sin-varphi-right2-b-fra\/","name":"According to Rankine's formula, minimum depth of foundations, is A. $$\\frac{{\\text{P}}}{{\\text{w}}} \\times {\\left( {\\frac{{1 + \\sin \\varphi }}{{1 - \\sin \\varphi }}} \\right)^2}$$ B. $$\\frac{{\\text{P}}}{{\\text{w}}} \\times {\\left( {\\frac{{1 - \\sin \\varphi }}{{1 + \\sin \\varphi }}} \\right)^2}$$ C. $$\\frac{{\\text{P}}}{{2{\\text{w}}}} \\times {\\left( {\\frac{{1 - \\sin \\varphi }}{{1 + \\sin \\varphi }}} \\right)^2}$$ D. $$\\frac{{\\text{P}}}{{\\text{w}}} \\times \\frac{{1 + \\sin \\varphi }}{{1 - \\sin \\varphi }}$$","isPartOf":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#website"},"datePublished":"2024-04-15T02:24:57+00:00","dateModified":"2024-04-15T02:24:57+00:00","author":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209"},"breadcrumb":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/according-to-rankines-formula-minimum-depth-of-foundations-is-a-fractextptextw-times-left-frac1-sin-varphi-1-sin-varphi-right2-b-fra\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/exam.pscnotes.com\/mcq\/according-to-rankines-formula-minimum-depth-of-foundations-is-a-fractextptextw-times-left-frac1-sin-varphi-1-sin-varphi-right2-b-fra\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/exam.pscnotes.com\/mcq\/according-to-rankines-formula-minimum-depth-of-foundations-is-a-fractextptextw-times-left-frac1-sin-varphi-1-sin-varphi-right2-b-fra\/#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":"Civil engineering","item":"https:\/\/exam.pscnotes.com\/mcq\/category\/mcq\/civil-engineering\/"},{"@type":"ListItem","position":4,"name":"Building construction","item":"https:\/\/exam.pscnotes.com\/mcq\/category\/mcq\/civil-engineering\/building-construction\/"},{"@type":"ListItem","position":5,"name":"According to Rankine&#8217;s formula, minimum depth of foundations, is A. $$\\frac{{\\text{P}}}{{\\text{w}}} \\times {\\left( {\\frac{{1 + \\sin \\varphi }}{{1 &#8211; \\sin \\varphi }}} \\right)^2}$$ B. $$\\frac{{\\text{P}}}{{\\text{w}}} \\times {\\left( {\\frac{{1 &#8211; \\sin \\varphi }}{{1 + \\sin \\varphi }}} \\right)^2}$$ C. $$\\frac{{\\text{P}}}{{2{\\text{w}}}} \\times {\\left( {\\frac{{1 &#8211; \\sin \\varphi }}{{1 + \\sin \\varphi }}} \\right)^2}$$ D. $$\\frac{{\\text{P}}}{{\\text{w}}} \\times \\frac{{1 + \\sin \\varphi }}{{1 &#8211; \\sin \\varphi }}$$"}]},{"@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\/6173"}],"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=6173"}],"version-history":[{"count":0,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts\/6173\/revisions"}],"wp:attachment":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/media?parent=6173"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/categories?post=6173"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/tags?post=6173"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}