{"id":9033,"date":"2018-02-08T16:24:17","date_gmt":"2018-02-08T10:54:17","guid":{"rendered":"http:\/\/mycbseguide.com\/blog\/?p=9033"},"modified":"2018-03-16T16:50:12","modified_gmt":"2018-03-16T11:20:12","slug":"mechanical-properties-of-solids-class-11-notes-physics","status":"publish","type":"post","link":"https:\/\/mycbseguide.com\/blog\/mechanical-properties-of-solids-class-11-notes-physics\/","title":{"rendered":"Mechanical Properties of Solids class 11 Notes Physics"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_76 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 eztoc-toggle-hide-by-default' ><ul class='ez-toc-list-level-2' ><li class='ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/mycbseguide.com\/blog\/mechanical-properties-of-solids-class-11-notes-physics\/#CBSE_Guide_Mechanical_Properties_of_Solids_class_11_Notes\" >CBSE Guide Mechanical Properties of Solids class 11 Notes<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/mycbseguide.com\/blog\/mechanical-properties-of-solids-class-11-notes-physics\/#11_Physics_notes_Chapter_9_Mechanical_Properties_of_Solids\" >11 Physics notes Chapter 9 Mechanical Properties of Solids<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-1'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/mycbseguide.com\/blog\/mechanical-properties-of-solids-class-11-notes-physics\/#Download_Revision_Notes_as_PDF\" >Download Revision Notes as PDF<\/a><ul class='ez-toc-list-level-2' ><li class='ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/mycbseguide.com\/blog\/mechanical-properties-of-solids-class-11-notes-physics\/#Mechanical_Properties_of_Solids_class_11_Notes\" >Mechanical Properties of Solids class 11 Notes<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/mycbseguide.com\/blog\/mechanical-properties-of-solids-class-11-notes-physics\/#CBSE_Class-11_Revision_Notes_and_Key_Points\" >CBSE Class-11 Revision Notes and Key Points<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<p>CBSE class 11 Physics Chapter 9 Mechanical Properties of Solids\u00a0 class 11 Notes Physics in PDF are available for free download in myCBSEguide mobile app. The best app for CBSE students now provides Mechanical Properties of Solids class 11 Notes\u00a0Physics latest chapter wise notes for quick preparation of CBSE exams and school based annual examinations.\u00a0 on Chapter 9 Mechanical Properties of Solids class 11 Notes Physics\u00a0 are also available for download in CBSE Guide website.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"CBSE_Guide_Mechanical_Properties_of_Solids_class_11_Notes\"><\/span>CBSE Guide Mechanical Properties of Solids class 11 Notes<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>CBSE guide notes are the comprehensive notes which covers the latest syllabus of CBSE and NCERT. It includes all the topics given in NCERT class 11 Physics text book. Users can download CBSE guide quick revision notes from myCBSEguide mobile app and my CBSE guide website.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"11_Physics_notes_Chapter_9_Mechanical_Properties_of_Solids\"><\/span>11 Physics notes Chapter 9 Mechanical Properties of Solids<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Download CBSE class 11th revision notes for Chapter 9 Mechanical Properties of Solids class 11 Notes Physics in PDF format for free. Download revision notes for Mechanical Properties of Solids class 11 Notes\u00a0Physics and score high in exams. These are the Mechanical Properties of Solids class 11 Notes\u00a0Physics prepared by team of expert teachers. The revision notes help you revise the whole chapter in minutes. Revising notes in exam days is on of the the best tips recommended by teachers during exam days.<\/p>\n<h1 style=\"text-align: center\"><span class=\"ez-toc-section\" id=\"Download_Revision_Notes_as_PDF\"><\/span><a href=\"https:\/\/mycbseguide.com\/downloads\/cbse-class-11-physics\/1340\/cbse-revision-notes\/7\/\">Download Revision Notes as PDF<\/a><span class=\"ez-toc-section-end\"><\/span><\/h1>\n<p style=\"text-align: center\"><strong>CBSE Class XI PHYSICS<br \/>\nRevision Notes<br \/>\nCHAPTER 9<br \/>\nMECHANICAL PROPERTIES OF SOLIDS<\/strong><\/p>\n<ul>\n<li><strong>Elastic behaviour of solids <\/strong><\/li>\n<li><strong>Stress and strain <\/strong><\/li>\n<li><strong>Hooke\u2019s law <\/strong><\/li>\n<li><strong>Young\u2019s modulus, bulk modulus, shear modulus of rigidity<\/strong><\/li>\n<li><strong>Poisson&#8217;s Ratio, Elastic Energy<\/strong><\/li>\n<\/ul>\n<p><strong>Deforming Force<\/strong>\u00a0: A force which produces a change in configuration of the object on applying it, is called a deforming force.<\/p>\n<p><strong>Elasticity<\/strong>: Elasticity is that property of the object by virtue of which it regain its original configuration after the removal of the deforming force.<\/p>\n<p><strong>Elastic Limit <\/strong>\u00a0: Elastic limit is the upper limit of deforming force upto which, if deforming force is removed, the body regains its original form completely and beyond which if deforming force is increased the body loses its property of elasticity and get permanently deformed.<\/p>\n<p><strong>Perfectly Elastic Bodies<\/strong>: Those bodies which regain its original configuration immediately and completely after the removal of deforming force are called perfectly elastic bodies. e.g., quartz and phosphor bronze etc.<\/p>\n<p><strong>Perfectly Plastic Bodies<\/strong>: Those bodies which does not regain its original configuration at all on the removal of deforming force are called perfectly plastic bodies, e.g., putty, paraffin, wax etc.<\/p>\n<p><strong>Stress <\/strong>: The internal restoring force acting per unit area of a deformed body is called stress.<\/p>\n<p>Stress = <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?Restoring \\ force \\over Area\" \/><\/span><\/span><\/p>\n<p>Its unit is N\/m<sup>2<\/sup> or Pascal and dimensional formula is[<span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?{\\text{M}}{{\\text{L}}^{ - 11}}{\\text{T}}{{\\text{ }}^{ - 2}}\" \/><\/span><\/span>].<\/p>\n<p>Stress is a tensor quantity.<\/p>\n<p><strong>Stress is of Two Types<\/strong><\/p>\n<p>(i) Normal Stress If deforming force is applied normal to the area, then the stress is called normal stress.<\/p>\n<p>If there is an increase in length, then stress is called <strong>tensile stress<\/strong>.<\/p>\n<p>If there is a decrease in length, then stress is <strong>called compression stress<\/strong>.<\/p>\n<p>(ii) <strong>Tangential Stress<\/strong> If deforming force is applied tangentially, then the stress is called tangential stress.<\/p>\n<p><strong>Strain <\/strong>: The fractional change in configuration is called strain.<\/p>\n<p>Strain = <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?Change \\ in \\ the \\ configuration \\over Original\\ configuration.\" \/><\/span><\/span><\/p>\n<p>It has no unit and it is a dimensionless quantity. According to the change in configuration, the strain is of three types<\/p>\n<p>(1) Longitudinal strain= <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?Change \\ in\\ length \\over Original\\ length\" \/><\/span><\/span><\/p>\n<p>(2) Volumetric strain = <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?Change\\ in\\ volume \\over Original\\ volume\" \/><\/span><\/span><\/p>\n<p>(iii) Shearing strain = Angular displacement of the plane perpendicular to the fixed surface.<\/p>\n<p><strong>Hooke\u2019s Law<\/strong><\/p>\n<p>Within the limit of elasticity, the stress is proportional to the strain.<\/p>\n<p>Stress &amp;infi; Strain<\/p>\n<p>or Stress = E * Strain<\/p>\n<p>where, E is the modulus of elasticity of the material of the body.<\/p>\n<p><strong>Types of Modulus of Elasticity <\/strong><\/p>\n<ol>\n<li><strong>Young\u2019s Modulus of Elasticity<\/strong><\/li>\n<\/ol>\n<p>It is defined as the ratio of normal stress to the longitudinal strain Within the elastic limit.<\/p>\n<p>y = Normal stress \/ Longitudinal strain<\/p>\n<p><span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?y = {F\\Delta \\over Al} = {Mg\\Delta l\\over \\pi r^2l}\" \/><\/span><\/span><\/p>\n<p>Its unit is N\/m<sup>2<\/sup> or Pascal and its dimensional formula is [<span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?{\\text{M}}{{\\text{L}}^{ - 2}}{\\text{T}}{{\\text{ }}^{ - 2}}\" \/><\/span><\/span>].<\/p>\n<p><strong>2. Bulk Modulus of Elasticity<\/strong><\/p>\n<p>It is defined as the ratio of normal stress to the volumetric strain within the elastic limit.<\/p>\n<p>K = <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?Normal \\ stress \\over Volumetric\\ strain\" \/><\/span><\/span><\/p>\n<p>K = <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?FV \\over A \u0394V\" \/><\/span><\/span>= \u0394p V \/ \u0394 V<\/p>\n<p>where, \u0394p = Change in pressure.<\/p>\n<p>Its unit is N\/m<sup>2<\/sup> or Pascal and its dimensional formula is [M<sup>-1<\/sup>T<sup>-2<\/sup> ].<\/p>\n<p>3. <strong>Modulus of Rigidity<\/strong> (\u03b7)<\/p>\n<p>It is defined as the ratio of tangential stress to the shearing strain, within the elastic limit.<\/p>\n<p>\u03b7 = Tangential stress \/ Shearing strain<\/p>\n<p>Its urut is N\/m<sup>2<\/sup> or Pascal and its dimensional formula is [ML<sup>-1<\/sup>T<sup>-2<\/sup> ].<\/p>\n<p><strong>Compressibility<\/strong><\/p>\n<p>Compressibility of a material is the reciprocal of its bulk modulus of elasticity. Compressibility (C) = 1 \/ k<\/p>\n<p>Its SI unit is N<sup>-1<\/sup>m<sup>2<\/sup> and CGS unit is dyne<sup>-1<\/sup> cm<sup>2<\/sup> . Steel is more elastic than rubber. Solids are more elastic and gases are least elastic. For liquids. modulus of rigidity is zero. Young\u2019s modulus (Y) and modulus of rigidity (\u03b7) are possessed by solid materials only.<\/p>\n<p><strong>Limit of Elasticity<\/strong><\/p>\n<p>The maximum value of deforming force for which elasticity is present in the body is called its limit of elasticity.<\/p>\n<p><strong>Breaking Stress<\/strong><\/p>\n<p>The minimum value of stress required to break a wire, is called breaking stress. Breaking stress is fixed for a material but breaking force varies with area of cross-section of the wire. Safety factor = <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?Breaking \\ stress \\over Working \\ stress\" \/><\/span><\/span><\/p>\n<p><strong>Elastic Relaxation Time<\/strong><\/p>\n<p>The time delay in restoring the original configuration after removal of deforming force is called elastic relaxation time.<\/p>\n<p>For quartz and phosphor bronze this time is negligible.<\/p>\n<p><strong>Elastic After Effect<\/strong><\/p>\n<p>The temporary delay in regaining the original configuration by the elastic body after the removal of deforming force, is called elastic after effect.<\/p>\n<p><strong>Elastic Fatigue<\/strong><\/p>\n<p>The property of an elastic body by virtue of which its behaviour becomes less elastic under the action of repeated alternating deforming force is called elastic fatigue.<\/p>\n<p><strong>Ductile Materials<\/strong><\/p>\n<p>The materials which show large plastic range beyond elastic limit are called ductile materials, e.g., copper, silver, iron, aluminum, etc. Ductile materials are used for making springs and sheets. Brittle Materials The materials which show very small plastic range beyond elastic limit are called brittle materials, e.g., glass, cast iron, etc.<\/p>\n<p><strong>Elastomers <\/strong><\/p>\n<p>The materials for which strain produced is much larger than the stress applied, with in the limit of elasticity are called elastomers, e.g., rubber, the elastic tissue of aorta, the large vessel carrying blood from heart. etc. Elastomers have no plastic range.<\/p>\n<p><strong>Elastic Potential Energy in a Stretched Wire<\/strong><\/p>\n<p>The work done in stretching a wire is stored in form of potential energy of the wire.<\/p>\n<p>Potential energy U = Average force * Increase in length<\/p>\n<p>=\u00a0<span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?{1 \\over 2} F\u0394l\" \/><\/span><\/span><\/p>\n<p>= <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?1 \\over2\" \/><\/span><\/span>Stress * Strain * Volume of the wire<\/p>\n<p>Elastic potential energy per unit volume<\/p>\n<p>U = <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?1 \\over 2\" \/><\/span><\/span>* Stress * Strain<\/p>\n<p>= <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?1 \\over 2\" \/><\/span><\/span>\u00a0(Young\u2019s modulus) * (Strain)<sup>2<\/sup><\/p>\n<p>Elastic potential energy of a stretched spring = <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?1 \\over 2\" \/><\/span><\/span>kx<sup>2<\/sup><\/p>\n<p>where, k = Force constant of spring and x = Change in length.<\/p>\n<p><strong>Thermal Stress<\/strong> When temperature of a rod fixed at its both ends is changed, then the produced stress is called thermal stress.<\/p>\n<p>Thermal stress = <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?F \\over A\" \/><\/span><\/span>\u00a0= y\u03b1\u0394\u03b8<\/p>\n<p>where, \u03b1 = coefficient of linear expansion of the material of the rod.<\/p>\n<p>When temperature of a gas enclosed in a vessel is changed, then the thermal stress produced is equal to change in pressure (\u0394p)of the gas.<\/p>\n<p>Thermal stress = \u0394 p = Ky \u0394 \u03b8<\/p>\n<p>where, K = bulk modulus of elasticity and<\/p>\n<p>\u03b3 = coefficient of cubical expansion of the gas.<\/p>\n<p>Interatomic force constant<\/p>\n<p>K = Yr<sub>o<\/sub><\/p>\n<p>where, r<sub>o<\/sub> = interatomic distance.<\/p>\n<p><strong>Poisson\u2019s Ratio<\/strong><\/p>\n<p>When a deforming force is applied at the free end of a suspended wire of length 1 and radius R, then its length increases by dl but its radius decreases by dR. Now two types of strains are produced by a single force.<\/p>\n<ol>\n<li>Longitudinal strain = \u0394Ul<\/li>\n<li>\u2234 Poisson\u2019s Ratio (\u03c3) = \u00a0= The theoretical value of Poisson\u2019s ratio lies between \u2013 1 and 0.5. Its practical value lies between 0 and 0.5<\/li>\n<\/ol>\n<p><strong>Relation Between Y, K, \u03b7 and \u03c3<\/strong><\/p>\n<p>(i) Y = 3K (1 \u2013 2\u03c3)<\/p>\n<p>(ii) Y = 2 \u03b7 ( 1 + \u03c3)<\/p>\n<p>Coefficient of elasticity depends upon the material, its temperature and purity but not on stress or strain.<\/p>\n<p>For the same material, the three coefficients of elasticity \u03b3, \u03b7 and K have different magnitudes.<\/p>\n<p>Isothermal elasticity of a gas ET = \u03c1 where, \u03c1 = pressure of the gas.<\/p>\n<p>Adiabatic elasticity of a gas Es = \u03b3\u03c1 where, \u03b3 = <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?C_p \\over C_v\" \/><\/span><\/span>; \u00a0ratio of specific heats at constant pressure and at constant volume<\/p>\n<p>Ratio between isothermal elasticity and adiabatic elasticity;\u00a0<span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi? {E_s \\over E_T }= \u03b3 = {C_p \\over C_v}\" \/><\/span><\/span><\/p>\n<p><strong>Cantilever<\/strong><br \/>\nA beam clamped at one end and loaded at free end is called a cantilever. Depression at the free end of a cantilever is given by<\/p>\n<p>\u03b4 = <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?wl^3 \\over 3YI^G\" \/><\/span><\/span><br \/>\n<img decoding=\"async\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/revise\/11\/physics\/11_Physics_revise_ch09_01.png\" \/><br \/>\nwhere, w = load, 1 = length of the cantilever,<br \/>\ny = Young\u2019s modulus of elasticity, and <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?{I^G}\" \/><\/span><\/span>\u00a0= geometrical moment of inertia.<br \/>\nFor a beam of rectangular cross-section having breadth b and thickness d.<br \/>\n<span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?I^G = {bd^3\\over 11}\" \/><\/span><\/span><br \/>\nFor a beam of circular cross-section area having radius r<br \/>\n<span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?I^G = {\u03c0 r^4 \\over4}\" \/><\/span><\/span><br \/>\nBeam Supported at Two Ends and Loaded at the Middle<br \/>\n<img decoding=\"async\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/revise\/11\/physics\/11_Physics_revise_ch09_02.png\" \/><br \/>\nDepression at middle \u03b4 = <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?wl^3 \\over 48YI^G\" \/><\/span><\/span><\/p>\n<p><strong>Torsion of a Cylinder<\/strong><br \/>\n<img decoding=\"async\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/revise\/11\/physics\/11_Physics_revise_ch09_03.png\" \/><br \/>\nwhere, \u03b7 = modulus of rigidity of the material of cylinder, r = radius of cylinder,<br \/>\nand 1 = length of cylinder,<br \/>\nWork done in twisting the cylinder through an angle \u03b8<br \/>\nW = 1 \/ 2 C\u03b82<br \/>\nRelation between angle of twist (\u03b8) and angle of shear (\u03c6) r\u03b8 = l\u03c6 or \u03c6 = r \/ l = \u03b8<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Mechanical_Properties_of_Solids_class_11_Notes\"><\/span>Mechanical Properties of Solids class 11 Notes<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<ul>\n<li>CBSE Revision notes (PDF Download) Free<\/li>\n<li>CBSE Revision notes for Class 11 Physics PDF<\/li>\n<li>CBSE Revision notes Class 11 Physics \u2013 CBSE<\/li>\n<li>CBSE Revisions notes and Key Points Class 11 Physics<\/li>\n<li>Summary of the NCERT books all chapters in Physics class 11<\/li>\n<li>Short notes for CBSE class 11th Physics<\/li>\n<li>Key notes and chapter summary of Physics class 11<\/li>\n<li>Quick revision notes for CBSE exams<br \/>\n<h2><span class=\"ez-toc-section\" id=\"CBSE_Class-11_Revision_Notes_and_Key_Points\"><\/span><strong>CBSE Class-11 Revision Notes and Key Points<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<\/li>\n<\/ul>\n<p>Mechanical Properties of Solids \u00a0class 11 Notes Physics. CBSE quick revision note for class-11 Physics, Chemistry, Maths, Biology and other subject are very helpful to revise the whole syllabus during exam days. The revision notes covers all important formulas and concepts given in the chapter. Even if you wish to have an overview of a chapter, quick revision notes are here to do if for you. These notes will certainly save your time during stressful exam days.<\/p>\n<ul>\n<li><a href=\"http:\/\/mycbseguide.com\/downloads\/cbse-class-11-physics\/1340\/cbse-revision-notes\/7\/\">Revision Notes for class-11 Physics<\/a><\/li>\n<li><a href=\"http:\/\/mycbseguide.com\/downloads\/cbse-class-11-chemistry\/1356\/cbse-revision-notes\/7\/\">Revision Notes for class-11 Chemistry<\/a><\/li>\n<li><a href=\"http:\/\/mycbseguide.com\/downloads\/cbse-class-11-mathematics\/1371\/cbse-revision-notes\/7\/\">Revision Notes for class-11 Mathematics<\/a><\/li>\n<li><a href=\"http:\/\/mycbseguide.com\/downloads\/cbse-class-11-biology\/1388\/cbse-revision-notes\/7\/\">Revision Notes for class-11 Biology<\/a><\/li>\n<li><a href=\"http:\/\/mycbseguide.com\/downloads\/cbse-class-11-accountancy\/1411\/cbse-revision-notes\/7\/\">Revision Notes for class-11 Accountancy<\/a><\/li>\n<li><a href=\"http:\/\/mycbseguide.com\/downloads\/cbse-class-11-economics\/1423\/cbse-revision-notes\/7\/\">Revision Notes for class-11 Economics<\/a><\/li>\n<li><a href=\"http:\/\/mycbseguide.com\/downloads\/cbse-class-11-business-studies\/1740\/cbse-revision-notes\/7\/\">Revision Notes for class-11 Business Studies<\/a><\/li>\n<li><a href=\"http:\/\/mycbseguide.com\/downloads\/cbse-class-11-computer-science\/1852\/cbse-revision-notes\/7\/\">Revision Notes for class-11 Computer Science<\/a><\/li>\n<li><a href=\"http:\/\/mycbseguide.com\/downloads\/cbse-class-11-informatics-practices\/1874\/cbse-revision-notes\/7\/\">Revision Notes for class-11 Informatics Practices<\/a><\/li>\n<li><a href=\"http:\/\/mycbseguide.com\/downloads\/cbse-class-11-geography\/1864\/cbse-revision-notes\/7\/\">Revision Notes for class-11 Geography<\/a><\/li>\n<\/ul>\n<p>To download Mechanical Properties of Solids class 11 Notes Physics, sample paper for class 11 Physics, Chemistry, Biology, History, Political Science, Economics, Geography, Computer Science, Home Science, Accountancy, Business Studies and Home Science; do check myCBSEguide app or website. myCBSEguide provides sample papers with solution, test papers for chapter-wise practice, NCERT solutions, NCERT Exemplar solutions, quick revision notes for ready reference, CBSE guess papers and CBSE important question papers. Sample Paper all are made available through\u00a0<a href=\"https:\/\/play.google.com\/store\/apps\/details?id=in.techchefs.MyCBSEGuide&amp;referrer=utm_source%3Dmycbse_bottom%26utm_medium%3Dtext%26utm_campaign%3Dmycbseads\"><strong>the best app for CBSE students<\/strong><\/a>\u00a0and myCBSEguide website.<\/p>\n<ul>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/physical-world-class-11-notes-physics\/\">Physical World class 11 Notes Physics<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/units-measurement-class-11-notes-physic\/\">Units and Measurement class 11 Notes Physics<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/8949-2\/\">Motion in a Straight Line class 11 Notes Physics<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/motion-in-a-plane-class-11-notes-physics\/\">Motion in a Plane class 11 Notes Physics<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/law-motion-class-11-notes-physics\/\">Law of Motion class 11 Notes Physics<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/work-energy-and-power-class-11-notes-physics\/\">Work, Energy and Power class 11 Notes Physics<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/systems-particles-rotational-motion-class-11-notes-physics\/\">Systems of Particles and Rotational Motion class 11 Notes Physics<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/gravitation-class-11-notes-physics\/\">Gravitation class 11 Notes Physics<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/mechanical-properties-of-solids-class-11-notes-physics\/\">Mechanical Properties of Solids class 11 Notes Physics<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/mechanical-properties-of-fluids-class-11-notes-physics\/\">Mechanical Properties of Fluids class 11 Notes Physics<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/thermal-properties-matter-class-11-notes-physics\/\">Thermal Properties of Matter class 11 Notes Physics<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/thermodynamics-class-11-notes-physics\/\">Thermodynamics class 11 Notes Physics<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/kinetic-theory-class-11-notes-physics\/\">Kinetic Theory class 11 Notes Physics<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/oscillations-class-11-notes-physics\/\">Oscillations class 11 Notes Physics<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/waves-class-11-notes-physics\/\">Waves class 11 Notes Physics<\/a><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>CBSE class 11 Physics Chapter 9 Mechanical Properties of Solids\u00a0 class 11 Notes Physics in PDF are available for free download in myCBSEguide mobile app. The best app for CBSE students now provides Mechanical Properties of Solids class 11 Notes\u00a0Physics latest chapter wise notes for quick preparation of CBSE exams and school based annual examinations.\u00a0 &#8230; <a title=\"Mechanical Properties of Solids class 11 Notes Physics\" class=\"read-more\" href=\"https:\/\/mycbseguide.com\/blog\/mechanical-properties-of-solids-class-11-notes-physics\/\" aria-label=\"More on Mechanical Properties of Solids class 11 Notes Physics\">Read more<\/a><\/p>\n","protected":false},"author":2,"featured_media":8931,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[47,456],"tags":[457,150,495,458,426,240],"class_list":["post-9033","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-cbse-class-11","category-revision-notes","tag-cbse-notes","tag-cbse-notes-and-key-points","tag-mechanical-properties-of-solids","tag-physics-notes","tag-quick-revision","tag-quick-revision-notes"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.0 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Mechanical Properties of Solids class 11 Notes Physics | myCBSEguide<\/title>\n<meta name=\"description\" content=\"Mechanical Properties of solids class 11 Notes Physics Chapter 9 in PDF format free download. 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