{"id":6703,"date":"2024-04-15T02:32:53","date_gmt":"2024-04-15T02:32:53","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=6703"},"modified":"2024-04-15T02:32:53","modified_gmt":"2024-04-15T02:32:53","slug":"two-forces-act-an-angle-of-120a-if-the-greater-force-is-50-kg-and-their-resultant-is-perpendicular-to-the-smaller-force-the-smaller-force-is-a-20-kg-b-25-kg-c-30-kg-d-35-kg","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/two-forces-act-an-angle-of-120a-if-the-greater-force-is-50-kg-and-their-resultant-is-perpendicular-to-the-smaller-force-the-smaller-force-is-a-20-kg-b-25-kg-c-30-kg-d-35-kg\/","title":{"rendered":"Two forces act an angle of 120\u00c2\u00b0. If the greater force is 50 kg and their resultant is perpendicular to the smaller force, the smaller force is A. 20 kg B. 25 kg C. 30 kg D. 35 kg"},"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_6a9a6945a6a2e\">\r\n                                            <div class=\"option\" data-option-key=\"option1\" data-is-correct=\"true\">\r\n                    20 kg                <\/div>\r\n                                            <div class=\"option\" data-option-key=\"option2\" data-is-correct=\"false\">\r\n                    25 kg                <\/div>\r\n                                            <div class=\"option\" data-option-key=\"option3\" data-is-correct=\"false\">\r\n                    30 kg                <\/div>\r\n                                            <div class=\"option\" data-option-key=\"option4\" data-is-correct=\"false\">\r\n                    35 kg                <\/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 $\\boxed{\\text{B) 25 kg}}$.<\/p>\n<p>Let $F_1$ be the greater force and $F_2$ be the smaller force. We know that $F_1 = 50$ kg and that the resultant force is perpendicular to the smaller force. This <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 <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> 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> means that the angle between $F_1$ and $F_2$ is $120^\\circ$.<\/p>\n<p>We can use the law of cosines to solve for $F_2$:<\/p>\n<p>$$F_2^2 = F_1^2 + F_2^2 &#8211; 2F_1F_2\\cos(120^\\circ)$$<\/p>\n<p>$$F_2^2 = 50^2 + F_2^2 &#8211; 2(50)(F_2)(-0.5)$$<\/p>\n<p>$$F_2^2 = 625 + 2F_2^2 + 50F_2$$<\/p>\n<p>$$F_2^2 &#8211; 50F_2 &#8211; 575 = 0$$<\/p>\n<p>$$(F_2 &#8211; 25)(F_2 + 23) = 0$$<\/p>\n<p>$$F_2 = 25\\text{ kg}$$ or $$F_2 = -23\\text{ kg}$$<\/p>\n<p>Since force is a vector, it has both magnitude and direction. The direction of the smaller force is unknown, so we cannot determine its magnitude. However, we can say that the magnitude of the smaller force is greater than or equal to 25 kg.<\/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>Two forces act an angle of 120\u00c2\u00b0. 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