Question

The potential energy for a force field $\overline{F}$ is given by $\cup$(x,y) = cos(x+y). The force acting on a particle at position given by coordinates (0, $\pi$/4) is

• A. - $\frac{1}{\sqrt{2}}$ $(\hat{i}+\hat{j})$
• B. $\frac{1}{\sqrt{2}}$ $(\hat{i}+\hat{j})$
• C. $($ $\frac{1}{2}$$\hat{i}$ + $\frac{\sqrt{3}}{2}$$\hat{j}$ $)$
• D. $($ $\frac{1}{2}$$\hat{i}$ - $\frac{\sqrt{3}}{2}$$\hat{j}$ $)$

Answer 1

The correct option is B

$\frac{1}{\sqrt{2}}$ $(\hat{i}+\hat{j})$

$F_x$ = - $\frac{\partial \cup }{\partial \chi }$ = sin(x + y) = $\frac{1}{\sqrt{2}}$

$F_y$ = - $\frac{\partial \cup }{\partial \gamma }$ = sin(x + y) = $\frac{1}{\sqrt{2}}$

$\overline{F}$ = $\frac{1}{\sqrt{2}}$ $[\hat{i}+\hat{j}]$