In the List-I below, four different paths of a particle are given as functions of time. In these functions, α and β are positive constants of appropriate dimension and α ≠ β . In each case, the force acting on the particle is either zero or conservative. In List-II, five physical quantitie

Question

In the List-I below, four different paths of a particle are given as functions of time. In these functions, α and β are positive constants of appropriate dimension and α ≠ β . In each case, the force acting on the particle is either zero or conservative. In List-II, five physical quantities of the particle are mentioned: p is the linear momentum, L is the angular momentum about the origin, K is the kinetic energy, U is the potential energy and E is the total energy. Match each path in List-I with those quantities in List-II, which are conserved for that path . LIST-I LIST-II P. ) t ( r G = α t i ˆ + β t j ˆ 1. p Q. ) t ( r G = α cos ω t i ˆ + β sin ω t j ˆ 2. L R. ) t ( r G = α (cos ω t i ˆ + sin ω t j ˆ ) 3. K S. ) t ( r G = α t i ˆ + 2 β t 2 j ˆ 4. U 5. E

Accepted Answer

P → 1, 2, 3, 4, 5; Q → 2, 5; R → 2, 3, 4, 5; S → 5

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