{"id":87966,"date":"2025-06-01T06:58:46","date_gmt":"2025-06-01T06:58:46","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=87966"},"modified":"2025-06-01T06:58:46","modified_gmt":"2025-06-01T06:58:46","slug":"a-railway-wagon-open-at-the-top-of-mass-m%e2%82%81-is-moving-with-speed-v%e2%82%81-a","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/a-railway-wagon-open-at-the-top-of-mass-m%e2%82%81-is-moving-with-speed-v%e2%82%81-a\/","title":{"rendered":"A railway wagon (open at the top) of mass M\u2081 is moving with speed v\u2081 a"},"content":{"rendered":"

A railway wagon (open at the top) of mass M\u2081 is moving with speed v\u2081 along a straight track. As a result of rain, after some time it gets partially filled with water so that the mass of the wagon becomes M\u2082 and speed becomes v\u2082. Taking the rain to be falling vertically and water stationary inside the wagon, the relation between the two speeds v\u2081 and v\u2082 is :<\/p>\n

[amp_mcq option1=”v\u2081 = v\u2082” option2=”1\/2 M\u2081v\u2081\u00b2 < 1\/2 M\u2082v\u2082\u00b2\" option3=\"M\u2081v\u2081 = M\u2082v\u2082\" option4=\"M\u2081v\u2081 < M\u2082v\u2082\" correct=\"option3\"]\n\n\n\n

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This question was previously asked in<\/div>\n
UPSC NDA-1 – 2023<\/div>\n<\/div>\n
Download PDF<\/a>Attempt Online<\/a><\/div>\n<\/div>\n
As the rain falls vertically, it has no horizontal momentum. The horizontal momentum of the system (wagon + water) is conserved because there are no external horizontal forces acting on it (assuming negligible friction and air resistance).<\/section>\n
The initial horizontal momentum of the wagon is $P_1 = M_1 v_1$. After the rain has collected, the total mass is $M_2$ and the speed is $v_2$. The final horizontal momentum is $P_2 = M_2 v_2$. By conservation of horizontal momentum, $P_1 = P_2$, so $M_1 v_1 = M_2 v_2$.<\/section>\n
This is an example of an inelastic collision\/process where mass is added to the system. Kinetic energy is not conserved in this case; the kinetic energy of the system decreases because the incoming water had zero horizontal kinetic energy relative to the ground.<\/section>\n","protected":false},"excerpt":{"rendered":"

A railway wagon (open at the top) of mass M\u2081 is moving with speed v\u2081 along a straight track. As a result of rain, after some time it gets partially filled with water so that the mass of the wagon becomes M\u2082 and speed becomes v\u2082. Taking the rain to be falling vertically and water … <\/p>\n

Detailed SolutionA railway wagon (open at the top) of mass M\u2081 is moving with speed v\u2081 a<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1093],"tags":[1105,1129,1128],"class_list":["post-87966","post","type-post","status-publish","format-standard","hentry","category-upsc-nda-1","tag-1105","tag-mechanics","tag-physics","no-featured-image-padding"],"yoast_head":"\nA railway wagon (open at the top) of mass M\u2081 is moving with speed v\u2081 a<\/title>\n<meta name=\"description\" content=\"As the rain falls vertically, it has no horizontal momentum. The horizontal momentum of the system (wagon + water) is conserved because there are no external horizontal forces acting on it (assuming negligible friction and air resistance). The initial horizontal momentum of the wagon is $P_1 = M_1 v_1$. After the rain has collected, the total mass is $M_2$ and the speed is $v_2$. The final horizontal momentum is $P_2 = M_2 v_2$. By conservation of horizontal momentum, $P_1 = P_2$, so $M_1 v_1 = M_2 v_2$.\" \/>\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\/a-railway-wagon-open-at-the-top-of-mass-m\u2081-is-moving-with-speed-v\u2081-a\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"A railway wagon (open at the top) of mass M\u2081 is moving with speed v\u2081 a\" \/>\n<meta property=\"og:description\" content=\"As the rain falls vertically, it has no horizontal momentum. The horizontal momentum of the system (wagon + water) is conserved because there are no external horizontal forces acting on it (assuming negligible friction and air resistance). The initial horizontal momentum of the wagon is $P_1 = M_1 v_1$. After the rain has collected, the total mass is $M_2$ and the speed is $v_2$. The final horizontal momentum is $P_2 = M_2 v_2$. By conservation of horizontal momentum, $P_1 = P_2$, so $M_1 v_1 = M_2 v_2$.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/exam.pscnotes.com\/mcq\/a-railway-wagon-open-at-the-top-of-mass-m\u2081-is-moving-with-speed-v\u2081-a\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ and Quiz for Exams\" \/>\n<meta property=\"article:published_time\" content=\"2025-06-01T06:58:46+00:00\" \/>\n<meta name=\"author\" content=\"rawan239\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"rawan239\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 minute\" \/>\n<!-- \/ Yoast SEO Premium plugin. -->","yoast_head_json":{"title":"A railway wagon (open at the top) of mass M\u2081 is moving with speed v\u2081 a","description":"As the rain falls vertically, it has no horizontal momentum. The horizontal momentum of the system (wagon + water) is conserved because there are no external horizontal forces acting on it (assuming negligible friction and air resistance). The initial horizontal momentum of the wagon is $P_1 = M_1 v_1$. After the rain has collected, the total mass is $M_2$ and the speed is $v_2$. The final horizontal momentum is $P_2 = M_2 v_2$. By conservation of horizontal momentum, $P_1 = P_2$, so $M_1 v_1 = M_2 v_2$.","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\/a-railway-wagon-open-at-the-top-of-mass-m\u2081-is-moving-with-speed-v\u2081-a\/","og_locale":"en_US","og_type":"article","og_title":"A railway wagon (open at the top) of mass M\u2081 is moving with speed v\u2081 a","og_description":"As the rain falls vertically, it has no horizontal momentum. The horizontal momentum of the system (wagon + water) is conserved because there are no external horizontal forces acting on it (assuming negligible friction and air resistance). The initial horizontal momentum of the wagon is $P_1 = M_1 v_1$. After the rain has collected, the total mass is $M_2$ and the speed is $v_2$. The final horizontal momentum is $P_2 = M_2 v_2$. 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