GATE 2024 MA – Question 35

Calculus · Vector Calculus · 1 mark · Numerical answer

Outward flux of F=(x³,y³,z³) through the unit sphere is απ. Find α to two decimals.

Show answer and explanation

Correct answer: 2.39 to 2.41

Explanation

Divergence is 3(x²+y²+z²)=3r². Gauss gives flux $\int_0^1 3r^2(4\pi r^2)dr=12\pi/5$. Therefore **α=2.40**.

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