Match the List I with the $$List-II$$ and select the correct answer using the code given below the lists.Three identical uniform rods each of mass ‘m’ and length ‘L’ are joined as shown in figure. The system is hinged about one end in a vertical plane. At equilibrium position, the value of '$$tan$$θ'isTwo identical uniform rods each of mass ‘m’ and length ‘L’ are joined as shown in figure. The system is hinged about one end in a vertical plane. At equilibrium position, the value of ‘$$tan$$θ’ isA ball is projected with velocity u at an angle ‘θ’ with the horizontal. The value of “$$tan$$θ” for which radius at the highest point is half the range is

Question

Match the List I with the $$List-II$$ and select the correct answer using the code given below the lists.Three identical uniform rods each of mass ‘m’ and length ‘L’ are joined as shown in figure. The system is hinged about one end in a vertical plane. At equilibrium position, the value of '$$tan$$θ'isTwo identical uniform rods each of mass ‘m’ and length ‘L’ are joined as shown in figure. The system is hinged about one end in a vertical plane. At equilibrium position, the value of ‘$$tan$$θ’ isA ball is projected with velocity u at an angle ‘θ’ with the horizontal. The value of “$$tan$$θ” for which radius at the highest point is half the range is

Infinity Learn · Accepted Answer

In equilibrium, the COM of system should lie vertically under the hinged point.$$P)$$ $$xcm=Ml2+Ml+Ml23M=2l3$$​$$ycm=M.0+Ml2+Ml3M=l2$$​$$tan$$ θ$$=ycmxcm=34under$$ $$equilibriumQ)$$ $$xcm=Ml2+Ml2M=3l4$$​$$ycm=M$$⋅$$0+Ml22M=l4$$​$$tan$$ θ$$=ycm/xcm=1/3R)$$ Perpendicular to plane, $$e=v$$ $$sin$$ θu $$cos$$ θ, ​Parallel to plane , u $$sin$$ θ$$=vcos$$ θ​⇒ $$v=u$$ $$tan$$ θ​∴$$e=tan2$$θ​⇒$$1/4$$ $$=tan2$$θ​⇒$$tan$$ θ$$=12S)$$ $$u2sin2$$θ$$2g=u2cos2$$θg​⇒ $$tan$$θ$$=1$$

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