Classical Mechanics MCQs with Answers 2027

Q41

A particle constrained to move along the X-axis in a potential V = kx², is subjected to an external time dependent force

F (t) .

Here, k is a constant, x, the distance from the origin and t is the time. At some time T, when the particle has zero velocity at x = 0, the external force is removed. The particle will

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Q42

Open question

A system of four particles is in X-Y plane of these two particles of masses m are located at (1, 1) and (-1, 1). The remaining two particles each of mass 2m are located at (1, 1) and (-1, -1). The xy component of moment of inertia tensor of the system of particles is

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Q43

Open question

A particle of mass m is constrained to move on the plane curve xy = c (c > 0) under gravity (Y-axis vertical). The Lagrangian of the particle is given by

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Q44

Open question

An electron gains energy so that its mass becomes 2m₀. Its speed is

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Q45

Open question

Let (p, q) and (P, Q) be two pairs of canonical variables. The transformation Q = q^α cos βp, P = q^α sin βp is canonical for

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Q46

Open question

Two bodies of masses m and 2m are connected by spring constant, the frequency of normal mode is

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Q47

Open question

A heavy symmetrical top is rotating about its own axis of symmetry (Z-axis). If

I_{1}, I_{2}

and

I_{3}

are the principal moments of inertia along X, Y and Z axes respectively then

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Q48

Open question

A hoop is pivoted at a point on circumference. The period of small oscillations in the plane of loop is

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Q49

Open question

The Lagrangian of a system is given by

L = \frac{1}{2} q ˙^{2} + q q ˙ - \frac{1}{2} q^{2}

It describes motion of a

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Q50

Open question

A particle of mass M moving in a straight line with speed v collides with a stationary particle of the same mass. In the centre of mass coordinate system, the first particle is deflected by 90°. The speed of second particle after collision in laboratory system will be

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Q51

Open question

In an electromagnetic field, which one of the following remains invariant under Lorentz transformation?

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Q52

Open question

A car is moving with constant linear acceleration a along horizontal X-axis. A solid sphere of mass M and radius R is found rolling without slipping on the horizontal floor of the car in the same direction as seen from an inertial frame outside the car. The acceleration of the sphere in the inertia frame is

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Q53

Open question

The Hamiltonian of a particle is

H = \frac{p ^{2}}{2 m} + pq,

where q is generalised coordinate and p is the corresponding canonical momentum. The Lagrangian is

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Q54

Open question

A rod of length L₀ makes an angle θ₀ with the Y-axis in its rest frame while the rest frame moves to the right along the X-axis with relativistic speed v with respect to lab frame. If

γ = (1 - \frac{v ^{2}}{c ^{2}})^{- \frac{1}{2}},

the angle in the lab frame is

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Q55

Open question

A particle of mass m moves in a potential V(x) =

\frac{1}{2}

mω²x² +

\frac{1}{2}

mμv², where x is the position coordinate, v is the speed and ω, μ are constants. The canonical momentum of the particle is

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Q56

Open question

For a particle moving in a central field,

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Q57

Open question

A particle of mass 2 kg is moving such that at time t second. Its position in metre is given by

r (t) = 5 i^- 2 t^{2} j^.

The angular momentum of the particle at t = 2 s about the origin in kg-m²/s, is

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Q58

Open question

The Lagrangian of a particle moving in a plane under the influence of central potential is given by

L = \frac{1}{2} m (r ˙^{2} = r^{2} θ ˙^{2}) - V (r) .

The generalised momenta corresponding to r and θ are given by

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Q59

Open question

The Lagrangian of a particle of mass m moving in a plane is given by L =

\frac{1}{2}

[m(v_x² + v_y²)] + a(xv_y - yv_x) where, v_x and v_y are velocity components and a is constant, The canonical momenta of the particle are given by

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Q60

Open question

Three particles of mass m each situated at x₁(t), x₂(t) and x₃(t) respectively are connected by two spring constants k and unstretched lengths

l

. The system is free to oscillate only in one-dimension along the straight line joining all the three particles. The Lagrangian of the system is

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Classical Mechanicspractice.

Classical Mechanics
practice.