Test: Classical Mechanics - 2 - Physics MCQ

# Test: Classical Mechanics - 2 - Physics MCQ

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## 20 Questions MCQ Test GATE Physics Mock Test Series 2025 - Test: Classical Mechanics - 2

Test: Classical Mechanics - 2 for Physics 2024 is part of GATE Physics Mock Test Series 2025 preparation. The Test: Classical Mechanics - 2 questions and answers have been prepared according to the Physics exam syllabus.The Test: Classical Mechanics - 2 MCQs are made for Physics 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Classical Mechanics - 2 below.
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Test: Classical Mechanics - 2 - Question 1

### For a system with one degree of freedom, hamiltonian is  The shape of x-t graph for the particle is

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Test: Classical Mechanics - 2 - Question 2

### A particle of charge q and rest mass m0 is kept at rest at the origin. A constant uniform electric field,  starts acting on it at t = 0. The speed of the particle at time t is (in the following c is speed of light)

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Test: Classical Mechanics - 2 - Question 3

### The Lagrangian of a system is  Which one of the following is conserved?

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Test: Classical Mechanics - 2 - Question 4

A pendulum consists of a mass m and a massless stick of length l. The pendulum support oscillates horizontally with a position given by x (t) = (see figure). The momentum conjugate to θ is

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The position of mass m is given by,

Test: Classical Mechanics - 2 - Question 5

If the Hamiltonian of a system with two degrees of freedom is given by

then the quantity that is conserved is

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Test: Classical Mechanics - 2 - Question 6

The Poisson bracket  with a and b as constants is equal to

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Test: Classical Mechanics - 2 - Question 7

A particle of effective mass m is acted on by a potential energy given by

where, u0, a and b are positive constants, then

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Test: Classical Mechanics - 2 - Question 8

The number of degrees of freedom of two particles moving on a space curve and having constant distance between them, is ______.

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Two particles in space have a combined six degrees of freedom; If two particles in space are constrained to maintain a constant distance from each other, such as in the case of a diatomic molecule, then the six coordinates must satisfy a single constraint equation defined by the distance formula.

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Test: Classical Mechanics - 2 - Question 9

The average lifetime of a π -meson in its own frame of reference is 26.011s. If the π - meson moves with speed 0.95c with respect to the earth, then the average distance it travels before decaying as measured byan observer at rest on Earth is approximately close to _______________________ meters (nearest integer)

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Lifetime measured by observer on earth.

The average distance it travels before decaying as measured byan observer at rest on Earth.

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Test: Classical Mechanics - 2 - Question 10

A particle of mass m is subjected to a central force given by the potential  The radius of the circular orbit for a particle with angular momentum,  The value of η is ______.

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Test: Classical Mechanics - 2 - Question 11

The path of a particle of mass m moving minder some potential V ( r ) is given by the r = A exp (aθ). where A and a are constants. The form of V(r) is (in the following L and E are angular momentum, and total energy, respectively)

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Test: Classical Mechanics - 2 - Question 12

A system with one degree of freedom has Lagrangian,  The equation of x(t) under the initial conditions t = 0, x = 0, p = mv0, is

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Test: Classical Mechanics - 2 - Question 13

The dynamics of a particle moving on the real line is determined by the Hamiltonian

where μ and λ are constants. Then the value of dp/dq is

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Test: Classical Mechanics - 2 - Question 14

Hamiltonian of a one dimensional dynamical system is given by

The Poisson bracket {p, H} is equal to

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Test: Classical Mechanics - 2 - Question 15

For a charged particle of mass m and charge e in a magnetic field  the Lagrangian is

The corresponding Hamiltonian is

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Test: Classical Mechanics - 2 - Question 16

Given that the linear transformation of a generalized coordinate q and corresponding momentum p,

is canonical, the value of the constant β is ______ (Here, i = √-1)

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Test: Classical Mechanics - 2 - Question 17

Two events in a inertial referance frame separated by a distance 3.6 x 108m and occur 2s apart. The proper time interval between the occurrence of these two events is _____ sec. (upto one decimal place)

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Consider an inertial reference frams S' moving relative to the given frame S (in equation) where the two events occurs at same spatial location,

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Test: Classical Mechanics - 2 - Question 18

The moment of inertia of a square frame of side length a and mass M about an axis passing through one of its
comers and perpendicular to its plane is βMa2. The value of β is________(upto two decimal places)

Detailed Solution for Test: Classical Mechanics - 2 - Question 18

The mass of the square frame is M
The sides ot square frame can be treated as rods ot mass 3/4 and length a.
Moment of inertia of one rod about an axis passing through its centre and perpendicular to its plane

Using parallel axis theorem, moment of inertia of the rod about an axis passing through centre of square frame and perpendicular to its plane.

By symmetry clue to all rock, total M.I.,

Now, using parallel axis theorem again, to find moment of inertia about the axis given in question,

*Answer can only contain numeric values
Test: Classical Mechanics - 2 - Question 19

Ail object of mass m = 100 kg and volume V= 0.18 m3 is dropped from a height h = 100m above the surface of the water. Upon entering water (β= 1000 kg/m3 ), the object experiences a resistance force given by F = -kv. where k = 10N sec in. The maximum depth to which the object will sink before starting to rise again is _____ m. (Neglect air resistance and assume the object looses negligible energy when going through the surface of the water). (Nearest integer)

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Let the velocity with which the object hits the water be

The equation of motion after it enters the water.

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Test: Classical Mechanics - 2 - Question 20

A star receding from the earth at a speed of 5 x 10-3c. The wavelength shift for the sodium D2 line is approximately equal to ____  (nearest integer)

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The Doppler equation gives,

Wavelength shift,

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