The GATE Grind

GATE 2022 MT – Question 23

Engineering Mathematics · Calculus and vector calculus · 1 mark · Multiple choice

A closed volume $V$ is bounded by surface $S$ with outward unit normal $\mathbf n$. For vector field $\mathbf f$ and gradient operator $\nabla$, which theorem gives $\int_V(\nabla\cdot\mathbf f)\,dV=\int_S(\mathbf n\cdot\mathbf f)\,dS$?

  1. Stokes Curl theorem
  2. Reynolds transport theorem
  3. Buckingham Pi theorem
  4. Gauss divergence theorem

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Correct answer: (D) Gauss divergence theorem

Explanation

The divergence theorem converts a volume integral of divergence to outward flux across its closed boundary: $\int_V\nabla\cdot\mathbf f\,dV=\int_S\mathbf f\cdot\mathbf n\,dS$. Answer: **Gauss divergence theorem, D**.