Question

Find out the potential energy of given force $\overrightarrow{F}=-2x\hat{i}-2y\hat{j}$ :

• A. $x^2+y^2+C$
• B. $x^2-y^2+C$
• C. $x^{2+C}+y^2$
• D. $x^{2+C}-y^2$

Answer 1

The correct option is A $x^2+y^2+C$

$dU=-dW$

$\int dU=\int -(-2x\hat{i}-2y\hat{j})\cdot (dx\hat{i}+dy\hat{j})$

$\int dU=\int 2xdx+\int 2ydy$

$\therefore U=x^2+y^2+C$