{"id":8110,"date":"2018-06-22T13:09:45","date_gmt":"2018-06-22T20:09:45","guid":{"rendered":"https:\/\/gurumuda.net\/physics\/?p=3149"},"modified":"2023-08-06T14:09:55","modified_gmt":"2023-08-06T14:09:55","slug":"dimensional-analysis-problems-and-solutions-2","status":"publish","type":"post","link":"https:\/\/gurumuda.net\/physics\/dimensional-analysis-problems-and-solutions-2.htm","title":{"rendered":"Dimensional analysis \u2013 problems and solutions","gt_translate_keys":[{"key":"rendered","format":"text"}]},"content":{"rendered":"

Dimensional analysis \u2013 problems and solutions<\/p>\n

1. <\/span><\/span>Based on the dimensional analysis, determine the following physics dimensions that have the same dimensions.<\/span><\/span><\/span><\/p>\n

A. work<\/a> and power<\/a><\/span><\/span><\/p>\n

B. power and pressure<\/span><\/span><\/p>\n

C. force and momentum<\/span><\/span><\/p>\n

D. work and heat<\/span><\/span><\/p>\n

Known :<\/u><\/span><\/span><\/p>\n

Dimension of length = dimension of width = dimension of displacement = L<\/span><\/span><\/p>\n

Dimension of time = T<\/span><\/span><\/p>\n

Dimension of mass = M<\/span><\/span><\/p>\n

Solution :<\/u><\/span><\/span><\/p>\n

Dimension of area = <\/span><\/span>dimension of length<\/span><\/span> x <\/span><\/span>dimension of width <\/span><\/span>= [L][L] = [L]<\/span><\/span>2<\/span><\/span><\/sup><\/p>\n

Dimension of velocity = <\/span><\/span>dimension of displacement<\/a><\/span><\/span> \/ <\/span><\/span>dimension of time<\/span><\/span> = [L] \/ [T] = [L][T]<\/span><\/span>-1<\/span><\/span><\/sup><\/p>\n

Dimension of acceleration <\/span><\/span>= <\/span><\/span>dimension of velocity<\/span><\/span> \/ <\/span><\/span>dimension of time <\/span><\/span>= [L][T]<\/span><\/span>-1 <\/span><\/span><\/sup>\/ [T] = [L][T]<\/span><\/span>-1<\/span><\/span><\/sup>[T]<\/span><\/span>-1<\/span><\/span><\/sup> = [L][T]<\/span><\/span>-2<\/span><\/span><\/sup><\/p>\n

Dimension of force<\/span><\/span> = <\/span><\/span>dimension of mass <\/span><\/span>x <\/span><\/span>dimension of acceleration<\/span><\/span> = [M][L][T]<\/span><\/span>-2<\/span><\/span><\/sup><\/p>\n

Dimension of work<\/span><\/span> = <\/span><\/span>dimension of force<\/span><\/span> x <\/span><\/span>dimension of displacement<\/span><\/span> = [M][L][T]<\/span><\/span>-2 <\/span><\/span><\/sup>[L] = [M][L]<\/span><\/span>2<\/span><\/span><\/sup>[T]<\/span><\/span>-2<\/span><\/span><\/sup><\/p>\n

Dimension of power<\/span><\/span> = <\/span><\/span>dimension of work<\/span><\/span> \/ <\/span><\/span>dimension of time<\/span><\/span> = [M][L]<\/span><\/span>2<\/span><\/span><\/sup>[T]<\/span><\/span>-2<\/span><\/span><\/sup> \/ [T] = [M][L]<\/span><\/span>2<\/span><\/span><\/sup>[T]<\/span><\/span>-2<\/span><\/span><\/sup>[T]<\/span><\/span>-1<\/span><\/span><\/sup> = [M][L]<\/span><\/span>2<\/span><\/span><\/sup>[T]<\/span><\/span>-3<\/span><\/span><\/sup><\/p>\n

Dimension of pressure<\/a><\/span><\/span> = <\/span><\/span>dimension of force<\/span><\/span> \/ <\/span><\/span>dimension of area<\/span><\/span> = [M][L][T]<\/span><\/span>-2<\/span><\/span><\/sup> \/ [L]<\/span><\/span>2 <\/span><\/span><\/sup>= [M][L][T]<\/span><\/span>-2 <\/span><\/span><\/sup>[L]<\/span><\/span>-2 <\/span><\/span><\/sup>= [M]<\/span><\/span> [L]<\/span><\/span>-1<\/span><\/span><\/sup>[T]<\/span><\/span>-2 <\/span><\/span><\/sup><\/p>\n

Dimension <\/span><\/span>of momentum <\/span><\/span>= <\/span><\/span>dimension of mass<\/span><\/span> x <\/span><\/span>dimension of velocity <\/span><\/span>= [M][L][T]<\/span><\/span>-1<\/span><\/span><\/sup><\/p>\n

Dimension of heat <\/span><\/span>= <\/span><\/span>dimension of energy <\/span><\/span>= <\/span><\/span>dimension of work <\/span><\/span>= [M][L]<\/span><\/span>2<\/span><\/span><\/sup>[T]<\/span><\/span>-2<\/span><\/span><\/sup><\/p>\n

The correct answer is <\/span><\/span>D.<\/span><\/span><\/p>\n

Note :<\/span><\/span><\/p>\n

Heat<\/a> is energy that moves due to the temperature difference.<\/span><\/span><\/p>\n

Work is the process of energy transfer through the displacement of objects.<\/span><\/span><\/p>\n

So, the dimension of heat = the dimension of energy = the dimension of work.<\/span><\/span><\/p>\n

2. Two quantities that have the same quantity but have a different physical concept\u2026<\/span><\/span><\/span><\/p>\n

A. Force and momentum<\/span><\/span><\/p>\n

B. Energy and force<\/span><\/span><\/p>\n

C. Potential energy and kinetic energy<\/span><\/span><\/p>\n

D. Energy and momentum<\/span><\/span><\/p>\n

Solution :<\/span><\/span><\/p>\n

Unit of potential energy = unit of kinetic energy<\/a> = unit of energy = unit of work.<\/span><\/span><\/p>\n

Although it has the sam<\/span>e <\/span>unit, but the potential energy and the kinetic energy are different types of energy.<\/span><\/span><\/span><\/p>\n

The correct answer is C.<\/span><\/span><\/p>\n

3. <\/span><\/span>The following quantities that have the same units are\u2026<\/span><\/span><\/p>\n

A. <\/span><\/span>Force and emf<\/span><\/span><\/p>\n

B. <\/span><\/span>Velocity and acceleration<\/span><\/span><\/p>\n

C. <\/span><\/span>Work and energy<\/span><\/span><\/p>\n

D. Work and power<\/span><\/span><\/p>\n

Solution :<\/span><\/span><\/p>\n

Work is the process of energy transfer through the displacement of objects.<\/span><\/span><\/p>\n

Energy is the ability to do work.<\/span><\/span><\/p>\n

Work and energy are two quantities of physics that have the same unit.<\/span><\/span><\/p>\n

The correct answer is C.<\/span><\/span><\/p>\n","protected":false,"gt_translate_keys":[{"key":"rendered","format":"html"}]},"excerpt":{"rendered":"

Dimensional analysis \u2013 problems and solutions 1. Based on the dimensional analysis, determine the following physics dimensions that have the same dimensions. A. work and power B. power and pressure C. force and momentum D. work and heat<\/p>\n","protected":false,"gt_translate_keys":[{"key":"rendered","format":"html"}]},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_seopress_titles_title":"","_seopress_titles_desc":"","_seopress_robots_index":"","_seopress_robots_follow":"","_seopress_robots_imageindex":"","_seopress_robots_snippet":"","_seopress_robots_primary_cat":"","_seopress_robots_breadcrumbs":"","_seopress_robots_freeze_modified_date":"","_seopress_robots_custom_modified_date":"","_seopress_robots_canonical":"","_seopress_social_fb_title":"","_seopress_social_fb_desc":"","_seopress_social_fb_img":"","_seopress_social_fb_img_attachment_id":0,"_seopress_social_fb_img_width":0,"_seopress_social_fb_img_height":0,"_seopress_social_twitter_title":"","_seopress_social_twitter_desc":"","_seopress_social_twitter_img":"","_seopress_social_twitter_img_attachment_id":0,"_seopress_social_twitter_img_width":0,"_seopress_social_twitter_img_height":0,"_seopress_redirections_value":"","_seopress_redirections_enabled":"","_seopress_redirections_enabled_regex":"","_seopress_redirections_logged_status":"","_seopress_redirections_param":"","_seopress_redirections_type":0,"_seopress_analysis_target_kw":"Dimensional analysis \u2013 problems and solutions","_seopress_news_disabled":"","_seopress_video_disabled":"","_seopress_video":[],"_seopress_pro_schemas_manual":[],"_seopress_pro_rich_snippets_disable_all":"","_seopress_pro_rich_snippets_disable":[],"_seopress_pro_schemas":[],"footnotes":""},"categories":[3],"tags":[],"class_list":["post-8110","post","type-post","status-publish","format-standard","hentry","category-solved-problems-in-basic-physics"],"gt_translate_keys":[{"key":"link","format":"url"}],"_links":{"self":[{"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/posts\/8110","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/comments?post=8110"}],"version-history":[{"count":1,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/posts\/8110\/revisions"}],"predecessor-version":[{"id":8524,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/posts\/8110\/revisions\/8524"}],"wp:attachment":[{"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/media?parent=8110"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/categories?post=8110"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/tags?post=8110"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}