Question

Which of the following forces is non conservative one?

• A. $3\hat{i}+4\hat{j}$
• B. $4x\hat{i}+3y\hat{j}$
• C. $3x^2\hat{i}+4y^2\hat{j}$
• D. $y^2\hat{i}+x^2\hat{j}$

Answer 1

The correct option is D

$y^2\hat{i}+x^2\hat{j}$

For conservative force $F_x=\frac{-dU}{dx};F_y=\frac{-dU}{dx}$
$\frac{\delta F_x}{\delta y}=\frac{\delta F_y}{\delta x}=\frac{{\delta }^{2}U}{\delta \times \delta y}$