Question

Consider a closed surface 'S' surrounding volume V. if $\overrightarrow{r}$ is the position vector of a point inside s with $\overrightarrow{n}$ the unit normal on 'S', the valuse of the integral $∯$$5\overrightarrow{r}.\hat{n}ds$ is

• A. 3V
• B. 5V
• C. 10V
• D. 15V

Answer 1

The correct option is D 15V

From Gauss Divergence Theorem
$∯$$\overrightarrow{F}.\hat{n}ds={\iiint }_{v}div\overrightarrow{F}dv$
$\Rightarrow$ $∯$5$\overrightarrow{r}.nds={\iiint }_{v}div\overrightarrow{r}dv$
= 5${\iiint }_v$(3)dv
=15V