First slide

Concept of potential energy

Question

The potential energy of a conservative force field is given by $U = 3 x^{2} y - 6 z$ .The force acting on particle is

Moderate

A

$6 x y \hat{i} + 3 x^{2} \hat{j} - 6 \hat{k}$
B

$- 6 x y \hat{i} + 3 x^{2} \hat{j} + 6 \hat{k}$
C

$6 x y \hat{i} - 3 x^{2} \hat{j} - 6 \hat{k}$
D

$- 6 x y \hat{i} - 3 x^{2} \hat{j} + 6 \hat{k}$

Solution

$\begin{array}{l} \vec{F} = \frac{- \partial U}{\partial x} \hat{i} - \frac{\partial U}{\partial y} \hat{j} - \frac{\partial U}{\partial z} \hat{k} \\ \vec{F} = - 6 x y \hat{i} - 3 x^{2} \hat{j} + 6 \hat{k} \end{array}$

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