Classical Mechanics Mock Tests

16 questions available

Classical Mechanics Mock Test 1

Questions: 16

Sample Questions

GATE Physics

In Rutherford scattering, the differential cross-section dσ/dΩ is proportional to:

A 1/sin⁴(θ/2)

B 1/sin²(θ/2)

C sin²(θ/2)

D 1/θ²

GATE Physics

The Lorentz transformation for time between two inertial frames moving with relative velocity v along the x-axis is:

A t' = γ(t - vx/c²)

B t' = γ(t + vx/c²)

C t' = t - vx/c²

D t' = γt

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

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 canonical transformation generated by the generating function F₂(q, P, t) satisfies:

A p = ∂F₂/∂q, Q = ∂F₂/∂P

B p = -∂F₂/∂q, Q = ∂F₂/∂P

C p = ∂F₂/∂q, Q = -∂F₂/∂P

D p = -∂F₂/∂q, Q = -∂F₂/∂P

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

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

For a conservative system, Lagrange's equations are derived from which variational principle?

A Cauchy's principle

B Hertz's principle

C Hamilton's principle

D D'Alembert's principle

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