{"id":6708,"date":"2024-04-15T02:32:58","date_gmt":"2024-04-15T02:32:58","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=6708"},"modified":"2024-04-15T02:32:58","modified_gmt":"2024-04-15T02:32:58","slug":"a-bullet-weighing-200-g-is-fired-horizontally-with-a-velocity-of-25-m-sec-from-a-gun-carried-on-a-carriage-which-together-with-the-gun-weighs-100-kg-the-velocity-of-recoil-of-the-gun-will-be-a-0-01","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/a-bullet-weighing-200-g-is-fired-horizontally-with-a-velocity-of-25-m-sec-from-a-gun-carried-on-a-carriage-which-together-with-the-gun-weighs-100-kg-the-velocity-of-recoil-of-the-gun-will-be-a-0-01\/","title":{"rendered":"A bullet weighing 200 g is fired horizontally with a velocity of 25 m\/sec from a gun carried on a carriage which together with the gun weighs 100 kg. The velocity of recoil of the gun, will be A. 0.01 m\/sec B. 0.05 m\/sec C. 1.00 m\/sec D. 1.5 m\/see"},"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_6a9abca701a8e\">\r\n                                            <div class=\"option\" data-option-key=\"option1\" data-is-correct=\"false\">\r\n                    0.01 m\/sec                <\/div>\r\n                                            <div class=\"option\" data-option-key=\"option2\" data-is-correct=\"false\">\r\n                    0.05 m\/sec                <\/div>\r\n                                            <div class=\"option\" data-option-key=\"option3\" data-is-correct=\"true\">\r\n                    1.00 m\/sec                <\/div>\r\n                                            <div class=\"option\" data-option-key=\"option4\" data-is-correct=\"false\">\r\n                    1.5 m\/see                <\/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 $\\boxed{\\text{B) 0.05 m\/sec}}$.<\/p>\n<p>According to the law of conservation of momentum, the total momentum of the system before the bullet is fired is equal to the total momentum of the system after the bullet is fired. In this case, the system consists of the bullet and the gun. The initial momentum of the system is zero, since the bullet and the gun are at rest. The final momentum of the system is the momentum of the bullet plus the momentum of the gun. The momentum of the bullet is <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> $p_b = mv_b = 0.2 \\text{ kg} \\times 25 \\text{ m\/s} = 5 \\text{ kg m\/s}$. The momentum of the gun is $p_g = mv_g$, where $v_g$ is the velocity of recoil of the gun. We can write the law of conservation of momentum as follows:<\/p>\n<p>$$p_b + p_g = 0$$<\/p>\n<p>$$5 \\text{ kg m\/s} + p_g = 0$$<\/p>\n<p>$$p_g = -5 \\text{ kg m\/s}$$<\/p>\n<p>The negative sign indicates that the velocity of recoil of the gun is in the opposite direction of the velocity of the bullet. The velocity of recoil of the gun is therefore $v_g = \\frac{p_g}{m_g} = \\frac{-5 \\text{ kg m\/s}}{100 \\text{ kg}} = -0.05 \\text{ m\/s}$.<\/p>\n<p>The other options <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> are incorrect because they do not give the correct value for the velocity of recoil of the gun.<\/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 bullet weighing 200 g is fired horizontally with a velocity of 25 m\/sec from a gun carried on a carriage which together with the gun weighs 100 kg. 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