GATE 2016 ME (ME3) – Question 37
Evaluate $\oint_C\mathbf F\cdot\mathbf r\prime\,ds$ on a counterclockwise circle of radius $4/\sqrt\pi$, where $\mathbf F(x,y)=y\hat i+2x\hat j$ and $\mathbf r\prime$ is the unit tangent at arc length s from a reference point.
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Correct answer: 15.9 to 16.1
Explanation
The tangent line integral is ∮(y dx+2x dy). By Green’s theorem its counterclockwise value is the area integral of ∂(2x)/∂x−∂y/∂y=1. The radius4/√π gives areaπ(16/π)=**16**. Reversing the stated orientation would change the sign.