GATE ME 2023 Set 1 — Question 31
Go beyond PYQs with Success TrackerAI-powered personalised practice and doubt support. Unlimited practice on eligible plans; AI usage limits apply.NAT+1 / -0MediumLine, Surface & Volume IntegralsVector CalculusEngineering MathematicsGauss Divergence Theorem
Engineering Mathematics → Vector Calculus → Gauss Divergence Theorem
Last updated
Question
A vector fieldis defined over a conical region having height , base radius and axis along , as shown in the figure. The base of the cone lies in the - plane and is centered at the origin. If denotes the unit outward normal to the curved surface of the cone, the value of the integralequals _________ . (Answer in integer)
Correct answer
0.001 to 0.001
Solution
According to the Gauss Divergence Theorem, the total outward flux of a vector field through a closed surface is equal to the volume integral of the divergence of over the region enclosed by the surface:First, calculate the divergence of :Since the divergence is zero everywhere, the total flux through the closed surface (consisting of the curved surface and the base ) is zero:On the base , the surface lies in the - plane () and the outward unit normal is .Thus, the flux through the base is:Substituting this back into the total flux equation:The value of the integral is 0.
Continue learning with Success Tracker
A step still unclear? Work through it with support
Use Success Tracker to ask about the reasoning, then try another GATE ME question to check your understanding.
AI-powered practice· Unlimited practice on eligible plans
- PYQs with solutions
- Attempt available previous-year questions, then compare your reasoning with the worked solution. Coverage varies by stream.
- Practice that adapts
- Choose a topic, work on weaker areas and bookmark questions to revisit. Your attempts feed your progress tracking.
- AI doubt support
- Ask follow-up questions about a step or concept while practising, instead of stopping at the final answer.
Unlimited practice is available on eligible plans. Free practice and AI usage have limits; check the current plan allowances before choosing.
This page stays readable without an account. AI responses can be wrong; check them against the solution and source material.
More questions on Vector Calculus
2026 Set 1 Q11Domain is bounded by curve , ordinate , and axis. The value of…2026 Set 1 Q12Let be a scalar function. Then, is2026 Set 1 Q13The order and degree of the following differential equation are and , respectively.…2026 Set 1 Q14Newton-Raphson method for solving algebraic equations is based on2026 Set 1 Q15The exact solution of is represented as . If represents…