{"id":6827,"date":"2024-04-15T02:34:45","date_gmt":"2024-04-15T02:34:45","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=6827"},"modified":"2024-04-15T02:34:45","modified_gmt":"2024-04-15T02:34:45","slug":"a-ladder-of-weight-w-rests-against-a-smooth-vertical-wall-and-rests-on-rough-horizontal-ground-the-coefficient-of-friction-between-the-ladder-and-the-ground-being-frac14-the-maximum-an","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/a-ladder-of-weight-w-rests-against-a-smooth-vertical-wall-and-rests-on-rough-horizontal-ground-the-coefficient-of-friction-between-the-ladder-and-the-ground-being-frac14-the-maximum-an\/","title":{"rendered":"A ladder of weight &#8216;w&#8217; rests against a smooth vertical wall and rests on rough horizontal ground, the coefficient of friction between the ladder and the ground being $$\\frac{1}{4}$$. The maximum angle of inclination of the ladder to the vertical, if a man of weight &#8216;w&#8217; is to walk to the top of it safely, is tan-1x, where x is A. $$\\frac{1}{4}$$ B. $$\\frac{1}{3}$$ C. 3 D. 4"},"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_6ab20169a393a\">\r\n                                            <div class=\"option\" data-option-key=\"option1\" data-is-correct=\"true\">\r\n                    $$\frac{1}{4}$$                <\/div>\r\n                                            <div class=\"option\" data-option-key=\"option2\" data-is-correct=\"false\">\r\n                    $$\frac{1}{3}$$                <\/div>\r\n                                            <div class=\"option\" data-option-key=\"option3\" data-is-correct=\"false\">\r\n                    3                <\/div>\r\n                                            <div class=\"option\" data-option-key=\"option4\" data-is-correct=\"false\">\r\n                    4                <\/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 $\\boxed{\\frac{1}{3}}$.<\/p>\n<p>The maximum angle of inclination of the ladder to the vertical is the angle at which the ladder is just about to slip. At this angle, the force of friction between the ladder and the ground is equal to the maximum possible force of friction, which is $\\mu N$, where $\\mu$ is the coefficient of friction and $N$ is the normal force. The normal force is equal to the weight of the ladder, $w$.<\/p>\n<p>The force of friction is also equal to the component of the weight of the ladder parallel to the ground, which is $w \\sin \\theta$, where $\\theta$ is the angle of inclination of the ladder to the vertical. Therefore, we have the equation<\/p>\n<p>$$\\mu N = w \\sin \\theta$$<\/p>\n<p>Substituting $N = w$, we get<\/p>\n<p>$$\\mu w = w \\sin \\theta$$<\/p>\n<p>Solving for $\\theta$, we get<\/p>\n<p>$$\\theta = \\sin^{-1} \\mu = \\sin^{-1} \\frac{1}{4} = \\boxed{\\frac{1}{3}}$$<\/p>\n<p>Option A is incorrect because the coefficient of friction is $\\frac{1}{4}$, not $\\frac{1}{3}$. Option B is incorrect because the angle of inclination of the ladder to the vertical is not $\\frac{1}{3}$ <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    <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>         <\/span>\r\n            Subscribe on YouTube\r\n        <\/a>\r\n    <\/div> radians. Option C is incorrect because the maximum angle of inclination of the ladder to the vertical is not 3 degrees. Option D is incorrect because the maximum angle of inclination of the ladder to the vertical is not 4 degrees.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Join Our Telegram Channel 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>A ladder of weight &#039;w&#039; rests against a smooth vertical wall and rests on rough horizontal ground, the coefficient of friction between the ladder and the ground being $$\\frac{1}{4}$$. The maximum angle of inclination of the ladder to the vertical, if a man of weight &#039;w&#039; is to walk to the top of it safely, is tan-1x, where x is A. $$\\frac{1}{4}$$ B. $$\\frac{1}{3}$$ C. 3 D. 4<\/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-ladder-of-weight-w-rests-against-a-smooth-vertical-wall-and-rests-on-rough-horizontal-ground-the-coefficient-of-friction-between-the-ladder-and-the-ground-being-frac14-the-maximum-an\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"A ladder of weight &#039;w&#039; rests against a smooth vertical wall and rests on rough horizontal ground, the coefficient of friction between the ladder and the ground being $$\\frac{1}{4}$$. The maximum angle of inclination of the ladder to the vertical, if a man of weight &#039;w&#039; is to walk to the top of it safely, is tan-1x, where x is A. $$\\frac{1}{4}$$ B. $$\\frac{1}{3}$$ C. 3 D. 4\" \/>\n<meta property=\"og:description\" content=\"Subscribe on YouTube\" \/>\n<meta property=\"og:url\" content=\"https:\/\/exam.pscnotes.com\/mcq\/a-ladder-of-weight-w-rests-against-a-smooth-vertical-wall-and-rests-on-rough-horizontal-ground-the-coefficient-of-friction-between-the-ladder-and-the-ground-being-frac14-the-maximum-an\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ and Quiz for Exams\" \/>\n<meta property=\"article:published_time\" content=\"2024-04-15T02:34:45+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 ladder of weight 'w' rests against a smooth vertical wall and rests on rough horizontal ground, the coefficient of friction between the ladder and the ground being $$\\frac{1}{4}$$. 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