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Work Power and Energy question

2018 · Shift 2 · Q53
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Work Power and Energy question

2018 · Shift 2 · Q53

JEE AdvancedPhysicsWork Power and EnergyMCQ+3 / −0.75
In the List-I{\rm I}I below, four different paths of a particle are given as functions of time. In these functions, α\alphaα and β\betaβ are positive constants of appropriate dimensions and αeβ\alpha e \betaαeβ In each case, the force acting on the particle is either zero or conservative. In List-II{\rm I}{\rm I}II, five physical quantities of the particle are mentioned p→\overrightarrow pp​ is the linear momentum, L→\overrightarrow LL is the angular momentum about the origin, KKK is the kinetic energy, UUU is the potential energy and EEE is the total energy. Match each path in List-I{\rm I}I with those quantities in List-II{\rm II}II, which are conserved for that path.

LIST - I LIST - II
P. r→\overrightarrow rr(t)=αt i^+βtj^\alpha t\,\widehat i + \beta t\widehat jαti+βtj​ 1. p→\overrightarrow pp​
Q. r→(t)=αcos⁡ ωt i^+βsin⁡ωt j^\overrightarrow r \left( t \right) = \alpha \cos \,\omega t\,\widehat i + \beta \sin \omega t\,\widehat jr(t)=αcosωti+βsinωtj​ 2. L→\overrightarrow LL
R. r→(t)=α(cos⁡ωt i^+sin⁡ωtj^)\overrightarrow r \left( t \right) = \alpha \left( {\cos \omega t\,\widehat i + \sin \omega t\widehat j} \right)r(t)=α(cosωti+sinωtj​) 3. K
S. r→(t)=αt i^+β2t2j^\overrightarrow r \left( t \right) = \alpha t\,\widehat i + {\beta \over 2}{t^2}\widehat jr(t)=αti+2β​t2j​ 4. U
5. E
  1. A
    P→1,2,3,4,5; Q→2,5;R→2,3,4,5;S→5P \to 1,2,3,4,5;\,Q \to 2,5;R \to 2,3,4,5;S \to 5P→1,2,3,4,5;Q→2,5;R→2,3,4,5;S→5
  2. B
    P→1,2,3,4,5; Q→3,5;R→2,3,4,5;S→2,5P \to 1,2,3,4,5;{\mkern 1mu} Q \to 3,5;R \to 2,3,4,5;S \to 2,5P→1,2,3,4,5;Q→3,5;R→2,3,4,5;S→2,5
  3. C
    P→2,3,4; Q→5;R→1,2,4;S→2,5P \to 2,3,4;{\mkern 1mu} Q \to 5;R \to 1,2,4;S \to 2,5P→2,3,4;Q→5;R→1,2,4;S→2,5
  4. D
    P→1,2,3,4,5; Q→2,5;R→2,3,4,5;S→2,5P \to 1,2,3,4,5;{\mkern 1mu} Q \to 2,5;R \to 2,3,4,5;S \to 2,5P→1,2,3,4,5;Q→2,5;R→2,3,4,5;S→2,5
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