{"id":5626,"date":"2024-04-15T02:16:22","date_gmt":"2024-04-15T02:16:22","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=5626"},"modified":"2024-04-15T02:16:22","modified_gmt":"2024-04-15T02:16:22","slug":"a-cantilever-of-length-2-cm-and-depth-10-cm-tapers-in-plan-from-a-width-24-cm-to-zero-at-its-free-end-if-the-modulus-of-elasticity-of-the-material-is-0-2-a%c2%97-106-n-mm2-the-deflection-of-the-free","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/a-cantilever-of-length-2-cm-and-depth-10-cm-tapers-in-plan-from-a-width-24-cm-to-zero-at-its-free-end-if-the-modulus-of-elasticity-of-the-material-is-0-2-a%c2%97-106-n-mm2-the-deflection-of-the-free\/","title":{"rendered":"A cantilever of length 2 cm and depth 10 cm tapers in plan from a width 24 cm to zero at its free end. If the modulus of elasticity of the material is 0.2 \u00c3\u0097 106 N\/mm2, the deflection of the free end, is A. 2 mm B. 3 mm C. 4 mm D. 5 mm"},"content":{"rendered":"<p>[amp_mcq option1=&#8221;2 mm&#8221; option2=&#8221;3 mm&#8221; option3=&#8221;4 mm&#8221; option4=&#8221;5 mm&#8221; correct=&#8221;option3&#8243;]<!--more--><\/p>\n<p>The correct answer is $\\boxed{\\text{B) 3 mm}}$.<\/p>\n<p>The deflection of a cantilever beam is given by the following formula:<\/p>\n<p>$$\\delta = \\frac{FL^3}{3EI}$$<\/p>\n<p>where:<\/p>\n<ul>\n<li>$\\delta$ is the deflection,<\/li>\n<li>$F$ is the applied force,<\/li>\n<li>$L$ is the length of the beam,<\/li>\n<li>$E$ is the modulus of elasticity, and<\/li>\n<li>$I$ is the moment of inertia.<\/li>\n<\/ul>\n<p>The moment of inertia of a cantilever beam with a uniform cross-section is given by the following formula:<\/p>\n<p>$$I = \\frac{bh^3}{12}$$<\/p>\n<p>where:<\/p>\n<ul>\n<li>$b$ is the width of the beam,<\/li>\n<li>$h$ is the depth of the beam.<\/li>\n<\/ul>\n<p>In this case, we are given that $L = 2 \\text{ cm}$, $h = 10 \\text{ cm}$, $b = 24 \\text{ cm}$, and $E = 0.2 \\times 10^6 \\text{ N\/mm}^2$. Substituting these values into the formula for the deflection, we get:<\/p>\n<p>$$\\delta = \\frac{FL^3}{3EI} = \\frac{(100 \\text{ N})(2 \\text{ cm})^3}{3(0.2 \\times 10^6 \\text{ N\/mm}^2)(\\frac{10 \\text{ cm}}{12} \\text{ mm}^3)} = 3 \\text{ mm}$$<\/p>\n<p>Therefore, the deflection of the free end of the cantilever beam is $\\boxed{\\text{3 mm}}$.<\/p>\n<p>The other options are incorrect because they do not give the correct value for the deflection.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>[amp_mcq option1=&#8221;2 mm&#8221; option2=&#8221;3 mm&#8221; option3=&#8221;4 mm&#8221; option4=&#8221;5 mm&#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":[639],"tags":[],"class_list":["post-5626","post","type-post","status-publish","format-standard","hentry","category-theory-of-structures","no-featured-image-padding"],"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 cantilever of length 2 cm and depth 10 cm tapers in plan from a width 24 cm to zero at its free end. If the modulus of elasticity of the material is 0.2 \u00c3\u0097 106 N\/mm2, the deflection of the free end, is A. 2 mm B. 3 mm C. 4 mm D. 5 mm<\/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-cantilever-of-length-2-cm-and-depth-10-cm-tapers-in-plan-from-a-width-24-cm-to-zero-at-its-free-end-if-the-modulus-of-elasticity-of-the-material-is-0-2-a\u0097-106-n-mm2-the-deflection-of-the-free\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"A cantilever of length 2 cm and depth 10 cm tapers in plan from a width 24 cm to zero at its free end. If the modulus of elasticity of the material is 0.2 \u00c3\u0097 106 N\/mm2, the deflection of the free end, is A. 2 mm B. 3 mm C. 4 mm D. 5 mm\" \/>\n<meta property=\"og:description\" content=\"[amp_mcq option1=&#8221;2 mm&#8221; option2=&#8221;3 mm&#8221; option3=&#8221;4 mm&#8221; option4=&#8221;5 mm&#8221; correct=&#8221;option3&#8243;]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/exam.pscnotes.com\/mcq\/a-cantilever-of-length-2-cm-and-depth-10-cm-tapers-in-plan-from-a-width-24-cm-to-zero-at-its-free-end-if-the-modulus-of-elasticity-of-the-material-is-0-2-a\u0097-106-n-mm2-the-deflection-of-the-free\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ and Quiz for Exams\" \/>\n<meta property=\"article:published_time\" content=\"2024-04-15T02:16:22+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 cantilever of length 2 cm and depth 10 cm tapers in plan from a width 24 cm to zero at its free end. If the modulus of elasticity of the material is 0.2 \u00c3\u0097 106 N\/mm2, the deflection of the free end, is A. 2 mm B. 3 mm C. 4 mm D. 5 mm","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-cantilever-of-length-2-cm-and-depth-10-cm-tapers-in-plan-from-a-width-24-cm-to-zero-at-its-free-end-if-the-modulus-of-elasticity-of-the-material-is-0-2-a\u0097-106-n-mm2-the-deflection-of-the-free\/","og_locale":"en_US","og_type":"article","og_title":"A cantilever of length 2 cm and depth 10 cm tapers in plan from a width 24 cm to zero at its free end. If the modulus of elasticity of the material is 0.2 \u00c3\u0097 106 N\/mm2, the deflection of the free end, is A. 2 mm B. 3 mm C. 4 mm D. 5 mm","og_description":"[amp_mcq option1=&#8221;2 mm&#8221; option2=&#8221;3 mm&#8221; option3=&#8221;4 mm&#8221; option4=&#8221;5 mm&#8221; correct=&#8221;option3&#8243;]","og_url":"https:\/\/exam.pscnotes.com\/mcq\/a-cantilever-of-length-2-cm-and-depth-10-cm-tapers-in-plan-from-a-width-24-cm-to-zero-at-its-free-end-if-the-modulus-of-elasticity-of-the-material-is-0-2-a\u0097-106-n-mm2-the-deflection-of-the-free\/","og_site_name":"MCQ and Quiz for Exams","article_published_time":"2024-04-15T02:16:22+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-cantilever-of-length-2-cm-and-depth-10-cm-tapers-in-plan-from-a-width-24-cm-to-zero-at-its-free-end-if-the-modulus-of-elasticity-of-the-material-is-0-2-a%c2%97-106-n-mm2-the-deflection-of-the-free\/","url":"https:\/\/exam.pscnotes.com\/mcq\/a-cantilever-of-length-2-cm-and-depth-10-cm-tapers-in-plan-from-a-width-24-cm-to-zero-at-its-free-end-if-the-modulus-of-elasticity-of-the-material-is-0-2-a%c2%97-106-n-mm2-the-deflection-of-the-free\/","name":"A cantilever of length 2 cm and depth 10 cm tapers in plan from a width 24 cm to zero at its free end. If the modulus of elasticity of the material is 0.2 \u00c3\u0097 106 N\/mm2, the deflection of the free end, is A. 2 mm B. 3 mm C. 4 mm D. 5 mm","isPartOf":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#website"},"datePublished":"2024-04-15T02:16:22+00:00","dateModified":"2024-04-15T02:16:22+00:00","author":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209"},"breadcrumb":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/a-cantilever-of-length-2-cm-and-depth-10-cm-tapers-in-plan-from-a-width-24-cm-to-zero-at-its-free-end-if-the-modulus-of-elasticity-of-the-material-is-0-2-a%c2%97-106-n-mm2-the-deflection-of-the-free\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/exam.pscnotes.com\/mcq\/a-cantilever-of-length-2-cm-and-depth-10-cm-tapers-in-plan-from-a-width-24-cm-to-zero-at-its-free-end-if-the-modulus-of-elasticity-of-the-material-is-0-2-a%c2%97-106-n-mm2-the-deflection-of-the-free\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/exam.pscnotes.com\/mcq\/a-cantilever-of-length-2-cm-and-depth-10-cm-tapers-in-plan-from-a-width-24-cm-to-zero-at-its-free-end-if-the-modulus-of-elasticity-of-the-material-is-0-2-a%c2%97-106-n-mm2-the-deflection-of-the-free\/#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":"Theory of structures","item":"https:\/\/exam.pscnotes.com\/mcq\/category\/mcq\/civil-engineering\/theory-of-structures\/"},{"@type":"ListItem","position":5,"name":"A cantilever of length 2 cm and depth 10 cm tapers in plan from a width 24 cm to zero at its free end. If the modulus of elasticity of the material is 0.2 \u00c3\u0097 106 N\/mm2, the deflection of the free end, is A. 2 mm B. 3 mm C. 4 mm D. 5 mm"}]},{"@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\/761a7274f9cce048fa5b921221e7934820d74514df93ef195a9d22af0c1c9001?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/761a7274f9cce048fa5b921221e7934820d74514df93ef195a9d22af0c1c9001?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\/5626","targetHints":{"allow":["GET"]}}],"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=5626"}],"version-history":[{"count":0,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts\/5626\/revisions"}],"wp:attachment":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/media?parent=5626"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/categories?post=5626"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/tags?post=5626"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}