Title K-2513 (Physical Science) (Paper-III) 16 page.pdf ✅

Total Number of Pages : 16 Paper III 4 K-2513 13. The canonical transformation corresponding to the generating function = ∑ i F qi pi (A) Identify transformation (B) Reflection transformation (C) Exchange transformation (D) Reflection exchange transformation 14. Which one of the following is not the generating function of the canonical transformation Q 1 P = and q = PQ2 (A) Q q (B) 2 qP (C) P P (D) P Q 15. Which of the following statements is false ? (A) The Poisson bracket of momentum conjugate to a cyclic co-ordinate with Hamiltonian vanishes (B) Lagrangian bracket is invariant under canonical transformations (C) Poisson bracket changes sign under commutation of concerned dynamical variables (D) Lagrangian bracket is commutative with respect to concerned dynamical variables 16. If (X, H) = 0 and (Y, H) = 0, the value of (H (X, Y)) is (A) 0 (B) 1 (C) –1 (D) 2 17. The value of (q p ) dt d i j is (A) Always zero (B) Always one (C) Zero when i ≠ j (D) Zero when i = j 18. If the Hamiltonian of a system is V(q) 2m p H 2 ⎟ + ⎠ ⎞ ⎜ ⎝ ⎛ = , the value of (p, (p, H)) is (A) Zero (B) One (C) 2 2 q v ∂ ∂ (D) q v ∂ ∂