GATE PH 2025 Paper 1 — page 18

Questions 52–54 of 65. Imported answers require review unless explicitly marked reviewed.

A bead is constrained to move along a long, massless, frictionless horizontal rod parallel to the

axis. The rod itself is moving vertically upward along the

direction against gravity with a constant speed, starting from

, and remains horizontal. The conjugate momenta are denoted by

and the Hamiltonian by

. Which of the following option(s) is/are correct?

Your answerSelect all correct options. You can choose more than one.

is the total energy of the system and is conserved

is the total energy of the system and is not conserved

is not the total energy of the system, but it is conserved

is not the total energy of the system and is not conserved

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In a one-dimensional Hamiltonian system with position

and momentum

, consider the canonical transformation

, where

and

are the new position and momentum, respectively. Which of the following option(s) regarding the generating function

is/are correct?

Your answerSelect all correct options. You can choose more than one.

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The energy of a free, relativistic particle of rest mass

moving along the

axis in one dimension, is denoted by

. When moving in a given potential

, its Hamiltonian is

. In the presence of this potential, its speed is

, conjugate momentum

, and the Lagrangian

. Then, which of the following option(s) is/are correct?

Your answerSelect all correct options. You can choose more than one.

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2025 · Paper 1