{"id":6798,"date":"2024-04-15T02:34:20","date_gmt":"2024-04-15T02:34:20","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=6798"},"modified":"2024-04-15T02:34:20","modified_gmt":"2024-04-15T02:34:20","slug":"from-a-solid-cylinder-of-height-8-cm-and-radius-4-cm-a-right-circular-cone-is-scooped-out-on-the-same-base-and-having-the-same-height-as-that-of-the-cylinder-the-c-g-of-the-remainder-is-at-a-height","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/from-a-solid-cylinder-of-height-8-cm-and-radius-4-cm-a-right-circular-cone-is-scooped-out-on-the-same-base-and-having-the-same-height-as-that-of-the-cylinder-the-c-g-of-the-remainder-is-at-a-height\/","title":{"rendered":"From a solid cylinder of height 8 cm and radius 4 cm, a right circular cone is scooped out on the same base and having the same height as that of the cylinder. The C.G. of the remainder is at a height of A. 4.5 cm B. 5.0 cm C. 5.25 cm D. 5.5 cm"},"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_6a9f6d82c5a95\">\r\n                                            <div class=\"option\" data-option-key=\"option1\" data-is-correct=\"true\">\r\n                    4.5 cm                <\/div>\r\n                                            <div class=\"option\" data-option-key=\"option2\" data-is-correct=\"false\">\r\n                    5.0 cm                <\/div>\r\n                                            <div class=\"option\" data-option-key=\"option3\" data-is-correct=\"false\">\r\n                    5.25 cm                <\/div>\r\n                                            <div class=\"option\" data-option-key=\"option4\" data-is-correct=\"false\">\r\n                    5.5 cm                <\/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 $\\boxed{\\text{B)} 5.0 \\text{ cm}}$.<\/p>\n<p>The center of mass (COM) of a solid cylinder is at its geometric center, which is at a height of $4 \\times \\frac{1}{2} = 2$ cm from the base. The COM of a right circular cone is at its apex, which is at a height of $4$ cm from the base.<\/p>\n<p>When <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            Subscribe on <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> YouTube\r\n        <\/a>\r\n    <\/div> the cone is scooped out of the cylinder, the COM of the remainder will be located somewhere between the COM of the cylinder and the COM of the cone, closer to the COM of the cylinder. This is because the cone has a smaller mass than the cylinder, so its COM will have a smaller effect on the overall COM of the remainder.<\/p>\n<p>To calculate the exact height of the COM of the remainder, we can use the following equation:<\/p>\n<p>$$h = \\frac{m_1 h_1 + m_2 h_2}{m_1 + m_2}$$<\/p>\n<p>where $h$ is the height of the COM of the remainder, $m_1$ is the mass of the cylinder, $h_1$ is the height of the cylinder, $m_2$ is the mass of the cone, and $h_2$ is the height of the cone.<\/p>\n<p>We know that $m_1 = \\pi r^2 h$, $m_2 = \\frac{1}{3} \\pi r^2 h$, $h_1 = 8$ cm, and $h_2 = 4$ cm. Substituting these values into the equation, we get:<\/p>\n<p>$$h = \\frac{\\pi (4)^2 (8) + \\frac{1}{3} \\pi (4)^2 (4)}{\\pi (4)^2 + \\frac{1}{3} \\pi (4)^2} = \\frac{32 + 16}{16 + 4} = 5.0 \\text{ cm}$$<\/p>\n<p>Therefore, the COM of the remainder is at a height of $5.0$ cm from the base.<\/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>From a solid cylinder of height 8 cm and radius 4 cm, a right circular cone is scooped out on the same base and having the same height as that of the cylinder. 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