Match the List I with the $$List-II$$ and select the correct answer using the code given below the lists. List – I List – IIThree 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. List – I List – IIThree 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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