{"id":6901,"date":"2024-04-15T02:35:51","date_gmt":"2024-04-15T02:35:51","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=6901"},"modified":"2024-04-15T02:35:51","modified_gmt":"2024-04-15T02:35:51","slug":"the-velocity-ratio-of-the-differential-wheel-and-axle-is-a-fractextrtextr_1-textr_2-b-frac2textrtextr_1-c-frac3textr","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/the-velocity-ratio-of-the-differential-wheel-and-axle-is-a-fractextrtextr_1-textr_2-b-frac2textrtextr_1-c-frac3textr\/","title":{"rendered":"The velocity ratio of the differential wheel and axle is A. $$\\frac{{\\text{R}}}{{{{\\text{r}}_1} &#8211; {{\\text{r}}_2}}}$$ B. $$\\frac{{2{\\text{R}}}}{{{{\\text{r}}_1}}}$$ C. $$\\frac{{3{\\text{R}}}}{{{{\\text{r}}_1} &#8211; {{\\text{r}}_2}}}$$ D. $$\\frac{{2{\\text{R}}}}{{{{\\text{r}}_1} + {{\\text{r}}_2}}}$$"},"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_6a972c0a0f9ba\">\r\n                                            <div class=\"option\" data-option-key=\"option1\" data-is-correct=\"false\">\r\n                    $$\frac{{\text{R}}}{{{{\text{r}}_1} - {{\text{r}}_2}}}$$                <\/div>\r\n                                            <div class=\"option\" data-option-key=\"option2\" data-is-correct=\"false\">\r\n                    $$\frac{{2{\text{R}}}}{{{{\text{r}}_1}}}$$                <\/div>\r\n                                            <div class=\"option\" data-option-key=\"option3\" data-is-correct=\"true\">\r\n                    $$\frac{{3{\text{R}}}}{{{{\text{r}}_1} - {{\text{r}}_2}}}$$                <\/div>\r\n                                            <div class=\"option\" data-option-key=\"option4\" data-is-correct=\"false\">\r\n                    $$\frac{{2{\text{R}}}}{{{{\text{r}}_1} + {{\text{r}}_2}}}$$                <\/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 $\\frac{{2{\\text{R}}}}{{{{\\text{r}}_1} + {{\\text{r}}_2}}}$.<\/p>\n<p>The velocity ratio of a differential wheel and axle is the ratio of the speed of the output shaft to the speed of the input shaft. It is calculated by dividing the radius of the output shaft by the sum of the radii of the input shafts.<\/p>\n<p>In the given question, the output shaft is the axle of the differential, and the input shafts are the axles of the wheels. The radius of the output shaft is ${\\text{R}}$, and the radii of the input shafts are ${\\text{r}}_1$ and ${\\text{r}}_2$. Therefore, the velocity ratio is:<\/p>\n<p>$$\\frac{{2{\\text{R}}}}{{{{\\text{r}}_1} + {{\\text{r}}_2}}}$$<\/p>\n<p>Option A is incorrect because it divides the radius of the output shaft by the difference of the radii of the input shafts. Option B is incorrect because it divides the radius of the output shaft by the radius of the <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 <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> 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> input shaft. Option C is incorrect because it divides the radius of the output shaft by the sum of the radii of the input shafts, but it is multiplied by 3.<\/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>The velocity ratio of the differential wheel and axle is A. $$\\frac{{\\text{R}}}{{{{\\text{r}}_1} - {{\\text{r}}_2}}}$$ B. $$\\frac{{2{\\text{R}}}}{{{{\\text{r}}_1}}}$$ C. $$\\frac{{3{\\text{R}}}}{{{{\\text{r}}_1} - {{\\text{r}}_2}}}$$ D. $$\\frac{{2{\\text{R}}}}{{{{\\text{r}}_1} + {{\\text{r}}_2}}}$$<\/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\/the-velocity-ratio-of-the-differential-wheel-and-axle-is-a-fractextrtextr_1-textr_2-b-frac2textrtextr_1-c-frac3textr\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"The velocity ratio of the differential wheel and axle is A. $$\\frac{{\\text{R}}}{{{{\\text{r}}_1} - 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{{\\text{r}}_2}}}$$ B. $$\\frac{{2{\\text{R}}}}{{{{\\text{r}}_1}}}$$ C. $$\\frac{{3{\\text{R}}}}{{{{\\text{r}}_1} - {{\\text{r}}_2}}}$$ D. $$\\frac{{2{\\text{R}}}}{{{{\\text{r}}_1} + {{\\text{r}}_2}}}$$","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\/the-velocity-ratio-of-the-differential-wheel-and-axle-is-a-fractextrtextr_1-textr_2-b-frac2textrtextr_1-c-frac3textr\/","og_locale":"en_US","og_type":"article","og_title":"The velocity ratio of the differential wheel and axle is A. $$\\frac{{\\text{R}}}{{{{\\text{r}}_1} - {{\\text{r}}_2}}}$$ B. $$\\frac{{2{\\text{R}}}}{{{{\\text{r}}_1}}}$$ C. $$\\frac{{3{\\text{R}}}}{{{{\\text{r}}_1} - {{\\text{r}}_2}}}$$ D. $$\\frac{{2{\\text{R}}}}{{{{\\text{r}}_1} + {{\\text{r}}_2}}}$$","og_description":"Join Our Telegram Channel Subscribe on YouTube","og_url":"https:\/\/exam.pscnotes.com\/mcq\/the-velocity-ratio-of-the-differential-wheel-and-axle-is-a-fractextrtextr_1-textr_2-b-frac2textrtextr_1-c-frac3textr\/","og_site_name":"MCQ and Quiz for Exams","article_published_time":"2024-04-15T02:35:51+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\/the-velocity-ratio-of-the-differential-wheel-and-axle-is-a-fractextrtextr_1-textr_2-b-frac2textrtextr_1-c-frac3textr\/","url":"https:\/\/exam.pscnotes.com\/mcq\/the-velocity-ratio-of-the-differential-wheel-and-axle-is-a-fractextrtextr_1-textr_2-b-frac2textrtextr_1-c-frac3textr\/","name":"The velocity ratio of the differential wheel and axle is A. $$\\frac{{\\text{R}}}{{{{\\text{r}}_1} - 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