Classical Mechanics MCQs with Answers 2027

Q21

For the given transformation
1. Q = p and P = -q
2. P = q and Q = p
where p, q are canonically conjugate variables, which one of the following statements is true?

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Q22

Open question

The Lagrangian for a simple pendulum is given by

L = \frac{1}{2} m L^{2} θ ˙^{2} - m g L (1 - cos θ)

Hamiltonian equations are given by

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Q23

Open question

Two events are separated by a distance of 6 × 10⁵ km and the first event occurs 1 s before the second event. The interval between two events is

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Q24

Open question

The lagrangian of a particle of mass m moving in one dimension is

L = exp [(α t) \frac{M x ˙ ^{2}}{2} - k x^{2}]

where,

α

and k are positive constants. The equation of motion of the particle is

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Q25

Open question

Although mass energy equivalence of special relativity allows conversion of a photon to an electron-positron pair, such a process cannot occur in free space because

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Q26

Open question

The Lagrangian forthe Kepler problem is given by

L = \frac{1}{2} [r ˙^{2} + r^{2} θ ˙^{2}] + \frac{μ}{r} (μ > 0)

where,

(r, θ)

denotes the polar coordinates and mass of the particle is unity, then

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Q27

Open question

For a simple harmonic oscillator, the Lagrangian is

L = \frac{1}{2} q ˙^{2} - \frac{1}{2} q^{2}, if A (p, q) = \frac{p + i q}{2}

and H(p, q) is the Hamiltonian of the system, the Poisson bracket, {A(p, q), H(p, q)} is given by

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Q28

Open question

A bead of mass m slides along a straight frictionless rigid wire rotating in a horizontal plane with a constant angular speed ω. The axis of rotation is perpendicular to the wire and passes through one end of the wire. If r is the distance of the mass from the axis of rotation and v is its speed, then the magnitude of the Coriolis force is

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Q29

Open question

If for a system of N particles of different masses m₁, m₂, . . . m_N with position vectors

r_{1}, r_{2}, . . . r_{N}

and corresponding velocities

v_{1}, v_{2}, . . . v_{N}

respectively such that

i \sum v_{i} = 0,

then

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Q30

Open question

The Lagrangian of a free particle in spherical polar coordinates is given by

L = \frac{1}{2} m [r ˙^{2} + r θ ˙^{2} + r^{2} ϕ ˙^{2} sin^{2} θ]

The quantity that conserved is

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Q31

Open question

Two particles of equal masses are connected by an inextensible string of length L. One of the masses is constrained to moves on the surface of a horizontal table. The string passes through a small hole in the table and the other mass is hanging below the table. The only constraint is that the first mass moves on the surface of the table. The number of degree of freedom of the masses string system is

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Q32

Open question

Assuming the mean life, of a muon (in its rest frame) to be 2 × 10^-6 s, its life time in the laboratory frame, when it is moving with a velocity 0.95 c is

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Q33

Open question

A particle is moving under the action of a generalised potential

V (q, q ˙) = \frac{( 1 + q ˙ )}{q ^{2}}

The magnitude of generalised force is

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Q34

Open question

The moment of inertia tensor of a rigid body is given by

I = \left[ {\begin{array}{*{20}{c}} 8&0&{ - 4} \\ 0&4&0 \\ { - 4}&0&8 \end{array}} \right]

Moment of inertia a out an axis

n^= (\frac{1}{2}, \frac{3}{2}, 0)

is

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Q35

Open question

A closed tall jar containing air and a fly placed on a sensitive weighing machine when the fly is stationary, the reading of the weighing machine is ω. If the fly starts with some upward acceleration, the reading of the machine will be

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Q36

Open question

Consider a comet of mass m moving in a parabolic orbit around the sun. The closets distance between the comet and the sun is b, the mass of the sun is M and universal gravitation constant is G. The angular momentum of the comet is

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Q37

Open question

The Lagrangian of two coupled oscillators of mass m each is

L = \frac{1}{2} (x ˙_{1}^{2} + x ˙_{2}^{2}) - \frac{1}{2} m ω_{0}^{2} (x_{1}^{2} + x_{2}^{2}) + m ω_{0}^{2} μ x_{1} x_{2}

The equations of motion are

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Q38

Open question

Which one of the following is true for the above system?

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Q39

Open question

A particle of mass m is moving in a potential of the form V(x, y, z) =

\frac{1}{2}

mω² (3x² + 3y² + 2z² + 2xy). The oscillation frequencies of the three normal modes of the particle are given by

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Q40

Open question

Consider two particles with position vectors

r_{1}

and

r_{2}

. The force exerted by particle 2 on particle 1 is

F (r_{1}, r_{2}) = (r ˙_{2} - r ˙_{1}) (r_{2} - r_{1}) .

The force is

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Classical Mechanicspractice.

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