Geodesic 1

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Geodesic 1

Each question carries 1 mark.

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1. If a curve satisfies the geodesic equation, it means

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The curve has no extrinsic curvature

The acceleration is purely normal to the surface

The covariant derivative of the velocity along itself is zero

The curve must be a straight line

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2. Which of the following is true for geodesics in Euclidean space?

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Geodesics are always curved

Geodesics are straight lines

Geodesics are defined using Gaussian curvature

Geodesics depend on the torsion tensor

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3. What is the Necessary and Sufficient Condition (NASC) for a curve to be a geodesic?

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The first derivative of the metric tensor must be zero

The curvature tensor must vanish along the curve

The Levi-Civita connection must be constant

The acceleration vector must be parallel to the tangent vector

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4. The geodesic equation in terms of the Lagrangian L is derived from which principle?

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Euler-Lagrange equations

Newton’s second law

Hamiltonian mechanics

Poisson’s equation

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5. In Riemannian geometry, geodesics are curves that

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Minimize the Euclidean distance

Are the shortest paths in the given metric space

Always have constant curvature

Are defined only in flat spaces

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6. A geodesic on a sphere is a

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Circle of any radius

Line of latitude

Great circle

Helix

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7. The geodesic equation in normal coordinates simplifies because

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The metric tensor is diagonal

Curvature vanishes

The coordinates are orthogonal

Christoffel symbols vanish at the origin

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8. If a geodesic equation is parameterized by the arc length s, which of the following is true?

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The velocity vector remains constant

The acceleration vector is perpendicular to the velocity vector

The covariant derivative of the velocity along itself is zero

The curve is always a straight line

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9. The geodesic equation can be derived from the variational principle applied to

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The action integral

The energy integral

The Hamiltonian function

The Newtonian force equation

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10. The geodesic deviation equation describes

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The change in curvature along a geodesic

How nearby geodesics converge or diverge

The motion of charged particles in a gravitational field

The variation of the metric tensor in normal coordinates

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