[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-670945-105":59,"doc-detail-670945-en":130},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":123,"head_meta":125,"extra_data":127,"updated_unix":129},105,"en","centre-of-gravity-and-centroid-applied-mechanics","CENTRE OF GRAVITY AND CENTROID - Applied Mechanics","","Centre of gravity and centroid calculations for symmetric and unsymmetric bodies are presented through worked examples and a structured problem set. The material includes centroidal distance computation from base, use of volume and centroidal distances (Vy), and final substitution to obtain y for composite solids. Definitions and key centroid locations for common shapes such as triangles, semicircles, cylinders, and cones are summarized, followed by objective fill-in-the-blank questions and exercises requiring derivations and numerical centroid determination for plane lamina and unsymmetrical sections.",{"@graph":69,"@context":122},[70,84,105],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":30,"@type":76,"position":81},"https://docshare.wps.com/document/technology/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/centre-of-gravity-and-centroid-applied-mechanics/670945/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/centre-of-gravity-and-centroid-applied-mechanics/670945.png","ImageObject",300,407,{"name":92,"@type":93},"mieayamfan","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-02","2026-11-01",true,{"@type":102,"interactionType":103,"userInteractionCount":8},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"How is centre of gravity related to weight and mass in this material?","Question",{"text":112,"@type":113},"Weight is defined as the force of attraction between a body and the earth and it is proportional to the mass of the body. The centre of gravity is the point through which the whole weight of the body may be assumed to act.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"What is the difference between centroid and centre of gravity?",{"text":117,"@type":113},"The centre of gravity concerns the action of the whole weight of a body, while the centroid (centre of area) is defined as the point where the whole area of the figure is assumed to be concentrated.",{"name":119,"@type":110,"acceptedAnswer":120},"Where do centroids of standard shapes like triangles and cylinders lie?",{"text":121,"@type":113},"A triangle’s centroid lies at intersection at h/3 from the base. A cylinder’s C.G. lies on the axis at a height one-half of the total height from the base.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},670945,1793573017,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":29,"category_name":30,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":8,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":139,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":129,"read_time":144},962090893677,"https://ap-avatar.wpscdn.com/davatar_3d24733baf745e90a7e4bdd5f77d97b2","CENTRE OF GRAVITY AND CENTROID 117  \nSince, the solid is symmetrical about y-axis, we shall out  y only with the following table :  \n\n| Components | Volume (mm3)\u003Cbr>V | Centroidal distance‘y’from base (mm) | Vy (mm4) |\n| --- | --- | --- | --- |\n| Cone (1)\u003Cbr>Cone (2) Cylinder (3) |  ~~ 1~~3 × π × 502 × 200 = 166666 π(+)\u003Cbr> ~~ 1~~3 × π × 252 × 100 = 20833 π(–)\u003Cbr>π × (12 .5)2 × 100 = 15625π (–) |  ~~ 20~~4~~0~~ = 50\u003Cbr> ~~ 10~~4~~0~~ + 100 = 125\u003Cbr>~~ 10~~2~~0~~ = 50 | 8333300π (+)\u003Cbr>2604125π (–)\u003Cbr>781250π (–) |\n| Total | ΣV = 130208π | — | ΣVy = 4947925π |\n\n∴  y = ~~ ~~ΣVyΣV = ~~ ~~4947925130208ππ = 38 mm. (Ans.)  \nHIGHLIGHTS  \n1. Weight is force of attraction between a body and the earth and is proportional to mass ofthe body.  \n2. Centre of gravity of the body is the point through which the whole weight of the body may be assumed to act.  \n3. The centre of gravity of some objects may be found by balancing the object on a point.  \n4. The centroid or centre of area is defined as the point where the whole area of the figure is assumed to be concentrated.  \n5. Centroid of a triangle lies at intersection of radius (h/3 from base) of the triangle.  \n6. Centroid of semi-circle lies at  ~~ 4~~3rπ = 0.424r from base, where r is radius of the semi-circle.  \n7. C.G. of a cylinder lies on the axis at a height one-half of the total height from the base.  \n8. C.G. of a solid cone lies on the axis at a height one-fourth of the total height from the base.  \n9. C.G. of thin hollow cone lies on the axis at a height one-third of the total height above the base.  \n10. C.G. of a solid hemisphere lies on the central radius at distance 3r/8 from the plane base, where r is radius of hemisphere.  \n11. C.G. of a hollow hemisphere bisects the central radius.  \nOBJECTIVE TYPE QUESTIONS  \nFill in the blanks :  \n(i)   is the force of attraction between a body and the earth and is proportional to mass ofthe body.  \n(ii) ...... is the point through which the whole weight of a body may be assumed to act.  \n(iii) ...... is the point where the whole area of the figure is assumed to be concentrated.  \n(iv) Centroid of a triangle lies at ....... from the base, where h is the height of triangle.  \n(v) Centroid of a semi-circle lies at a distance of   from the base, where r is the radius of semi-circle.  \n(vi) Area of a quadrant is given by ......, where r is the radius.  \n(vii) C.G. of a cylinder lies on the axis at a height ...... of the total height from the base.  \n(viii) C.G. of a solid cone lies on the axis at a height ...... of the total height from the base.  \n(ix) C.G. of a hollow cone lies on the axis at a height ...... of the total height above the base.  \n(x) C.G. of a solid hemisphere lies on the central radius at a distance   from the plane base, where ris the radius of hemisphere.  \n118 APPLIED MACHANICS  \nAnswers  \n(i) Weight (ii) Centre of gravity (iii) Centroid (iv) h/3  \n(v) 0 .424r (vi) πr2/4 (vii) h/2 (viii) one-fourth  \n(ix) h/3 (x)  ~~ 3~~r8 .  \nEXERCISES  \nTheoretical Questions  \n1. Define the terms ‘Centre of gravity’ and ‘Centroid’.  \n2. Explain briefly how centre of gravity of a body can be determined.  \n3. Write down the positions of centroids of the following plane geometrical figures :  \nRectangle, circle, semi-circle, quadrant and trapezium.  \n4. Where do the C.Gs ofthe following regular solids lie ?  \nCylinder, sphere, hemisphere, right circular cone.  \n5. Derive expressions for centre of gravity in the following cases :  \n(i) Solid right circular cone  \n(ii) Thin hollow right circular cone  \n(iii) Semi-circular lamina.  \nUnsolved Examples  \n1. Locate the centroid of the piece of sheet metal shown in Fig. 4.43. [Ans.  x  = 4.59 cm,  y = 3.19 cm]  \n3 cm  \n| 4 cm | 3 cm |\n| --- | --- |\n\nFig. 4.43  \n2. Find the centroid ofthe lamina shown in Fig. 4.44. [Ans.  x  = 2.50 cm,  y = 3.50 cm]  \nFig. 4.44  \nCENTRE OF GRAVITY AND CENTROID 119  \n3. Find the centroid ofthe lamina shown in Fig. 4.45. [Ans.  y = 1.864 cm from the bottom]  \nFig","cbCaif9wfMcn9mh5","https://ap.wps.com/l/cbCaif9wfMcn9mh5","pdf",346258,31,"English","# Highlights\n## Objective Type Questions\n## Exercises\n### Theoretical Questions\n### Unsolved Examples","[{\"question\":\"How is centre of gravity related to weight and mass in this material?\",\"answer\":\"Weight is defined as the force of attraction between a body and the earth and it is proportional to the mass of the body. The centre of gravity is the point through which the whole weight of the body may be assumed to act.\"},{\"question\":\"What is the difference between centroid and centre of gravity?\",\"answer\":\"The centre of gravity concerns the action of the whole weight of a body, while the centroid (centre of area) is defined as the point where the whole area of the figure is assumed to be concentrated.\"},{\"question\":\"Where do centroids of standard shapes like triangles and cylinders lie?\",\"answer\":\"A triangle’s centroid lies at intersection at h/3 from the base. A cylinder’s C.G. lies on the axis at a height one-half of the total height from the base.\"}]","CENTRE OF GRAVITY AND CENTROID - Applied Mechanics | PDF",78]