GATE PH Classical Mechanics PYQs & Answers — Page 2

Questions 11–20 of 51. Imported answers require independent review unless marked reviewed.

A particle of mass 1 kg is released from a height of 1 m above the ground. When it reaches the ground, what is the value of Hamilton’s action for this motion in J s? (

is the acceleration due to gravity; take gravitation potential to be zero on the ground)

Your answerChoose one option.

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

is a constant of motion of a two-dimensional isotropic harmonic oscillator with Lagrangian

then

Your answerChoose one option.

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

A particle of unit mass moves in a potential

. If the angular momentum of the particle is

, then which of the following statements are true?

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

There are two equilibrium points along the radial coordinate

There is one stable equilibrium point at

and one unstable equilibrium point at

There are two stable equilibrium points along the radial coordinate

There is only one equilibrium point along the radial coordinate

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

A system with time independent Hamiltonian

has two constants of motion

and

. Then which of the following Poisson brackets are always zero?

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

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

In the action-angle variables

, consider the Hamiltonian

and

. Let

. Which of the following are possible plots of the trajectories with different initial conditions in

plane?

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

Diagram for Physics question 55 (figure 2)

Diagram for Physics question 55 (figure 3)

Diagram for Physics question 55 (figure 4)

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

Two identical particles of rest mass

approach each other with equal and opposite velocity

, where

is the speed of light. The total energy of one particle as measured in the rest frame of the other is

. The value of

is ______________ (Round off to two decimal places)

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

Two observers

and

observe two events

and

. The observers have a constant relative speed of 0.5c. In the units, where the speed of light, c, is taken as unity, the observer

obtained the following coordinates:

Event

The length of the space-time interval between these two events, as measured by

, is

. The value of

(in integer) is ______.

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

A hoop of mass

and radius

rolls without slipping along a straight line on a horizontal surface as shown in the figure. A point mass

slides without friction along the inner surface of the hoop, performing small oscillations about the mean position. The number of degrees of freedom of the system (in integer) is _____.

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

Consider a point charge

of mass

suspended by a mass, inextensible string of length

in free space (permittivity

) as shown in the figure. It is placed at a height

(

) over an infinitely large, grounded conducting plane. The gravitational potential energy is assumed to be zero at the position of the conducting plane and is positive above the plane. If

represents the angular position and

its corresponding canonical momentum, then the correct Hamiltonian of the system is

Your answerChoose one option.

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

Consider a spherical galaxy of total mass

and radius

, having a uniform matter distribution. In this idealized situation, the orbital speed

of a star of mass

(

) as a function of the distance

from the galactic centre is best described by

(

is the universal gravitational constant)

Your answerChoose one option.

Diagram for Physics question 39 (figure 2)

Diagram for Physics question 39 (figure 3)

Diagram for Physics question 39 (figure 4)

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

GATE PH Classical Mechanics PYQs

Question 41

Question 42

Question 49

Question 54

Question 55

Question 61

Question 18

Question 20

Question 30

Question 39