Classical Mechanics Mock Tests

16 questions available

Classical Mechanics Mock Test 1

Questions: 16

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GATE Physics

The relativistic energy-momentum relation is:

A E² = (pc)² + (m₀c²)²

B E = pc + m₀c²

C E² = (pc)² - (m₀c²)²

D E = p²c² + m₀²c⁴

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

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

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

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

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 Lagrangian for a charged particle of mass m and charge q in an electromagnetic field (with scalar potential φ and vector potential A) is:

A L = (1/2)mv² - qφ + qv·A

B L = (1/2)mv² - qφ - qv·A

C L = (1/2)mv² + qφ - qv·A

D L = (1/2)mv² - q(φ + A)

Classical Mechanics Mock Tests

Classical Mechanics Mock Test 1

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