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A particle in a certain conservative force field has a potential energy given by $U = \frac{20 xy}{z}$ . The force exerted on it is

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$- (\frac{20 y}{z}) \hat{i} - (\frac{20 x}{z}) \hat{j} + (\frac{20 xy}{z^{2}}) \hat{k}$

$- (\frac{20 y}{z}) \hat{i} - (\frac{20 x}{z}) \hat{j} - (\frac{20 xy}{z^{2}}) \hat{k}$

$(\frac{20 y}{z}) \hat{i} + (\frac{20 x}{z}) \hat{j} + (\frac{20 xy}{z^{2}}) \hat{k}$

$(\frac{20 y}{z}) \hat{i} + (\frac{20 x}{z}) \hat{j} - (\frac{20 xy}{z^{2}}) \hat{k}$

answer is B.

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Detailed Solution

$\vec{F} = - (\frac{\partial U}{\partial x} \hat{i} + \frac{\partial U}{\partial y} \hat{j} + \frac{\partial U}{\partial z} \hat{k}) = - (\frac{20 y}{z}) \hat{i} - (\frac{20 x}{z}) \hat{j} + (\frac{20 xy}{z^{2}}) \hat{k}$

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