GATE PH topic:classical-mechanics PYQs & Answers — Page 4

Questions 31–40 of 51. Imported answers require independent review unless marked reviewed.

During a rotation, vectors along the axis of rotation remain unchanged. For the rotation matrix

the unit vector along the axis of rotation is

Your answerChoose one option.

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Consider a transformation from one set of generalized coordinate and momentum

to another set

denoted by,

where

and

are constants. The transformation is canonical if

Your answerChoose one option.

and

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The Hamiltonian for a particle of mass

where

and

are the generalized coordinate and momentum, respectively,

is time and

is a constant. For the initial condition,

and

. The value of

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A ball bouncing off a rigid floor is described by the potential energy function

Which of the following schematic diagrams best represents the phase space plot of the ball?

Your answerChoose one option.

Diagram for Physics question 38 (figure 2)

Diagram for Physics question 38 (figure 3)

Diagram for Physics question 38 (figure 4)

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Consider the Hamiltonian

, where

and

are parameters with appropriate dimensions, and

and

are the generalized coordinate and momentum, respectively. The corresponding Lagrangian

Your answerChoose one option.

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A projectile of mass 1 kg is launched at an angle of 30° from the horizontal direction at

and takes time

before hitting the ground. If its initial speed is 10 ms

, the value of the action integral for the entire flight in the units of kg m

(rounded off to one decimal place) is [Take

]

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Two spaceships A and B, each of the same rest length

, are moving in the same direction with speeds

and

, respectively, where

is the speed of light. As measured by B, the time taken by A to completely overtake B [see figure below]

in units of

(to the nearest integer) is

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Two events, one on the earth and the other one on the Sun, occur simultaneously in the earth’s frame. The time difference between the two events as seen by an observer in a spaceship moving with velocity

in the earth’s frame along the line joining the earth to the Sun is

, where

is the speed of light. Given that light travels from the Sun to the earth in 8.3 minutes in the earth’s frame, the value of

in minutes (rounded off to two decimal places) is ______

(Take the earth’s frame to be inertial and neglect the relative motion between the earth and the sun)

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In the context of small oscillations, which one of the following does NOT apply to the normal coordinates?

Your answerChoose one option.

Each normal coordinate has an eigen-frequency associated with it

The normal coordinates are orthogonal to one another

The normal coordinates are all independent

The potential energy of the system is a sum of squares of the normal coordinates with constant coefficients

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A spaceship is traveling with a velocity of 0.7c away from a space station. The spaceship ejects a probe with a velocity 0.59c opposite to its own velocity. A person in the space station would see the probe moving at a speed Xc, where the value of X is ________ (up to three decimal places).

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GATE PH topic:classical-mechanics PYQs

Question 8

Question 10

Question 22

Question 38

Question 42

Question 45

Question 47

Question 54

Question 6

Question 19