Classical Mechanics Mock Tests

16 questions available

Classical Mechanics Mock Test 1

Questions: 16

Sample Questions

GATE Physics

The action S in Lagrangian mechanics is defined as:

A S = ∫L dt from t₁ to t₂

B S = ∫T dt from t₁ to t₂

C S = ∫V dt from t₁ to t₂

D S = L · (t₂ - t₁)

GATE Physics

Hamilton's equations of motion are given by which of the following?

A ḋqᵢ = ∂H/∂pᵢ, ḋpᵢ = -∂H/∂qᵢ

B ḋqᵢ = -∂H/∂pᵢ, ḋpᵢ = ∂H/∂qᵢ

C ḋqᵢ = ∂H/∂qᵢ, ḋpᵢ = ∂H/∂pᵢ

D ḋqᵢ = -∂H/∂qᵢ, ḋpᵢ = -∂H/∂pᵢ

JEE Advanced Physics

A body of mass m is tied to one end of a string of length L and whirled in a vertical circle. The minimum velocity at the lowest point to complete the circle is:

A √(5gL)

B √(3gL)

C √(2gL)

D √(gL)

GATE Physics

Liouville's theorem in classical statistical mechanics states that:

A The volume of phase space occupied by an ensemble of systems is conserved along trajectories

B The total energy of a system is always conserved

C The entropy of an isolated system never decreases

D Momentum is conserved in elastic collisions

GATE Physics

Liouville's theorem in classical mechanics states that the phase space density:

A is constant along a trajectory

B increases with time

C decreases with time

D oscillates periodically

GATE Physics

The Poisson bracket of two functions f(q, p) and g(q, p) in classical mechanics is defined as:

A {f, g} = Σᵢ(∂f/∂qᵢ · ∂g/∂pᵢ - ∂f/∂pᵢ · ∂g/∂qᵢ)

B {f, g} = Σᵢ(∂f/∂qᵢ · ∂g/∂qᵢ - ∂f/∂pᵢ · ∂g/∂pᵢ)

C {f, g} = Σᵢ(∂f/∂pᵢ · ∂g/∂pᵢ + ∂f/∂qᵢ · ∂g/∂qᵢ)

D {f, g} = Σᵢ(∂f/∂qᵢ · ∂g/∂pᵢ + ∂f/∂pᵢ · ∂g/∂qᵢ)

GATE Physics

The Schwarzschild radius R_S of a black hole of mass M is:

A 2GM/c²

B GM/c²

C 2GMc²

D GM/(2c²)

GATE Physics

In Hamiltonian mechanics, action-angle variables (J, θ) are particularly useful for:

A Integrable systems with periodic motion

B Chaotic systems with irregular trajectories

C Relativistic systems only

D Systems with time-dependent Hamiltonians

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