{"id":6791,"date":"2024-04-15T02:34:13","date_gmt":"2024-04-15T02:34:13","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=6791"},"modified":"2024-04-15T02:34:13","modified_gmt":"2024-04-15T02:34:13","slug":"a-stone-of-mass-1-kg-is-tied-to-a-string-of-length-1-m-and-whirled-in-a-horizontal-circle-at-a-constant-angular-speed-5-rad-sec-the-tension-in-the-string-is-a-5-n-b-10-n-c-15-n-d-25-n","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/a-stone-of-mass-1-kg-is-tied-to-a-string-of-length-1-m-and-whirled-in-a-horizontal-circle-at-a-constant-angular-speed-5-rad-sec-the-tension-in-the-string-is-a-5-n-b-10-n-c-15-n-d-25-n\/","title":{"rendered":"A stone of mass 1 kg is tied to a string of length 1 m and whirled in a horizontal circle at a constant angular speed 5 rad\/sec. The tension in the string is, A. 5 N B. 10 N C. 15 N D. 25 N"},"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_6a9f0ff47eb0b\">\r\n                                            <div class=\"option\" data-option-key=\"option1\" data-is-correct=\"false\">\r\n                    5 N                <\/div>\r\n                                            <div class=\"option\" data-option-key=\"option2\" data-is-correct=\"false\">\r\n                    10 N                <\/div>\r\n                                            <div class=\"option\" data-option-key=\"option3\" data-is-correct=\"true\">\r\n                    15 N                <\/div>\r\n                                            <div class=\"option\" data-option-key=\"option4\" data-is-correct=\"false\">\r\n                    25 N                <\/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 $\\boxed{\\text{B. 10 N}}$.<\/p>\n<p>The centripetal force on the stone is given by $F_c = \\frac{mv^2}{r}$, where $m$ is the mass of the stone, $v$ is the velocity of the stone, and $r$ is the radius of the circle. The velocity of the stone is given by $v = \\omega r$, where $\\omega$ is the angular speed of the stone. The angular speed is given by $\\omega = 2\\pi f$, where $f$ is the frequency of <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 YouTube\r\n        <\/a>\r\n    <\/div> the circular motion. The frequency is given by $f = \\frac{1}{T}$, where $T$ is the period of the circular motion.<\/p>\n<p>The period <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> of the circular motion is given by $T = \\frac{2\\pi}{v}$. Substituting this into the equation for the centripetal force, we get $F_c = \\frac{m(2\\pi f)^2}{r}$. Substituting in the values for $m$, $f$, and $r$, we get $F_c = \\frac{(1 \\text{ kg})(2\\pi (5 \\text{ rad\/s})^2}{(1 \\text{ m})} = 10 \\text{ N}$.<\/p>\n<p>Option A is incorrect because it is the centripetal force on the stone if the stone were moving at a constant speed. However, the stone is moving in a circular path, so the centripetal force is constantly changing.<\/p>\n<p>Option C is incorrect because it is the centripetal force on the stone if the string were not attached to anything. However, the string is attached to something, so the centripetal force is not equal to the weight of the stone.<\/p>\n<p>Option D is incorrect because it is the centripetal force on the stone if the string were twice as long. However, the string is only 1 m long, so the centripetal force is not equal to 25 N.<\/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 stone of mass 1 kg is tied to a string of length 1 m and whirled in a horizontal circle at a constant angular speed 5 rad\/sec. 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