Question

The potential energy for a force field $\overline{F}$ is given by $U(x,y)=sin(x+y)$. The force acting on the particle mass $m$at $(0,\frac{\pi }{4})$ is

• A. $1$
• B. $\sqrt{2}$
• C. $\frac{1}{\sqrt{2}}$
• D. $0$

Answer 1

The correct option is A $1$

$\overrightarrow{F}(x,y)=\frac{\partial U}{\partial x}\hat{x}+$$\frac{\partial U}{\partial y}\hat{y}=\cos (x+y)(\hat{x}+\hat{y})$

$\Rightarrow \overrightarrow{F}(0,\frac{\pi }{4})=\frac{1}{\sqrt{2}}(\hat{x}+\hat{y})$

$\Rightarrow |\overrightarrow{F}(0,\frac{\pi }{4})|=\frac{1}{\sqrt{2}}\sqrt{1^2+1^2}=1$

Hence, correct answer is option $A$