Question:
The value of the surface integral
\(\displaystyle\oiint_{s}zdxdy\)
where S is the external surface of the sphere x2 + y2 + z2 = R2 is
The value of the surface integral
\(\displaystyle\oiint_{s}zdxdy\)
where S is the external surface of the sphere x2 + y2 + z2 = R2 is
\(\displaystyle\oiint_{s}zdxdy\)
where S is the external surface of the sphere x2 + y2 + z2 = R2 is
Updated On: Jan 10, 2025
- 0
- 4πR3
- \(\frac{4\pi}{3}R^3\)
- πR3
Hide Solution
Verified By Collegedunia
The Correct Option is C
Solution and Explanation
The correct option is (C): \(\frac{4\pi}{3}R^3\)
Was this answer helpful?
1
2
Top Questions on Vector identities
Consider designing a linear binary classifier \( f(x) = \text{sign}(w^T x + b), x \in \mathbb{R}^2 \) on the following training data:
Class-2: \( \left\{ \left( \begin{array}{c} 0 \\ 0 \end{array} \right) \right\} \)
Hard-margin support vector machine (SVM) formulation is solved to obtain \( w \) and \( b \). Which of the following options is/are correct?- GATE DA - 2025
- Engineering Mathematics
- Vector identities
- If \( \nabla \phi = 2xy^2 \hat{i} + x^2z^2 \hat{j} + 3x^2y^2z^2 \hat{k} \), then \( \phi(x,y,z) \) is:
- TANCET - 2024
- Engineering Mathematics
- Vector identities
- Three vectors \(\vec{p},\vec{q}\ \text{and}\ \vec{r}\) are given as
\(\vec{p}=\hat{i}+\hat{j}+\hat{k}\)
\(\vec{q}=\hat{i}+2\hat{j}+3\hat{k}\)
\(\vec{r}=2\hat{i}+3\hat{j}+4\hat{k}\)
Which of the following is/are CORRECT ?- GATE CE - 2024
- Mathematics
- Vector identities
- A vector field \(\vec p\) and a scalar field \(r\) are given by
\(\vec p=(2x^2-3xy+z^2)\hat i+(2y^2−3yz+x^2)\hat j+(2z^2−3xz+x^2)\hat k\)
\(r=6x^2+4y^2 - z^2-9xyz - 2xy + 3xz-yz\)
Consider the statements P and Q.
P: Curl of the gradient of the scalar field r is a null vector.
Q: Divergence of curl of the vector field p is zero.
Which one of the following options is CORRECT?- GATE CE - 2024
- Mathematics
- Vector identities
Questions Asked in GATE Metallurgy exam
- Let f(z) be an analytic function, where z = x + iy. If the real part of f(z) is cosh x cos y, and the imaginary part of f(z) is zero for y = 0, then f(z) is
- GATE Metallurgy - 2024
- Analytic functions
- Steady, compressible flow of air takes place through an adiabatic converging- diverging nozzle, as shown in the figure. For a particular value of pressure difference across the nozzle, a stationary normal shock wave forms in the diverging section of the nozzle. If E and F denote the flow conditions just upstream and downstream of the normal shock, respectively, which of the following statement(s) is/are TRUE?
- GATE Metallurgy - 2024
- Basics of compressible fluid flow
- In an arc welding process, the voltage and current are 30V and 200A, respectively. The cross-sectional area of the joint is 20 mm2 and the welding speed is 5mm/s. The heat required to melt the material is 20 J/s. The percentage of heat lost to the surrounding during the welding process is ____(rounded off to 2 decimal places).
- GATE Metallurgy - 2024
- Principles of welding, brazing, soldering and adhesive bonding
- A set of jobs U, V, W, X, Y, Z arrive at time t = 0 to a production line consisting of two workstations in series. Each job must be processed by both workstations in sequence (i.e., the first followed by the second). The process times (in minutes) for each job on each workstation in the production line are given below.
Job U V W X Y Z Workstation 1 5 7 3 4 6 8 Workstation 2 4 6 6 8 5 7
The sequence in which the jobs must be processed by the production line if the total makespan of production is to be minimized is- GATE Metallurgy - 2024
- Principles of non-traditional machining processes
- A ram in the form of a rectangular body of size l=9m and b=2m is suspended by two parallel ropes of lengths 7m. Assume the center-of-mass of the body is at its geometric center and g = 9.81m/s2. For striking the object P with a horizontal velocity of 5m/s, what is the angle θ with the vertical from which the ram should be released from rest?
- GATE Metallurgy - 2024
- Forces on submerged bodies
View More Questions