In the List-I below, four different paths of a particle are given as functions of time. In these functions, α a n d β are positive constants of appropriate dimensions 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

Step-by-step solution

( i ) r → t = α t i ^ + β t j ^ v → = d r → t d t = α i ^ + β j ^ constant a → = d v → d t = 0 P → = m v → (remain constant) k = 1 2 m v 2 remain constant F → = - ∂ U ∂ x i ^ + ∂ U ∂ y i ^ = 0 ⇒ U → constant E = K + U d L → d t = - τ → = r → × F → = 0 L → = constant ( i i ) r → = α cos ⁡ ω t i ^ + β sin ⁡ ω t j ^ v → = d r → d t = - α ω sin ⁡ ω t i ^ + β ω cos ⁡ ω t j ^ a → = d v → d t = - α ω 2 cos ⁡ ω t i ^ + β ω sin ⁡ ⁡ ω t j ^ = - ω 2 α cos ⁡ ω t i ^ + β sin ⁡ ω t j ^ a → = = - α ω 2 τ → = r → × F → = 0 r → a n