A particle in a certain conservative force filed has a potential energy given by $V = \frac{20 x y}{z}$ . The force exerted on it is

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

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

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

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

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Solution

The correct option is B $- (\frac{20 y}{z})^i - (\frac{20 x}{z})^j + (\frac{20 x y}{z^{2}})^k$
$F = - \frac{δ V}{δ x}^i - \frac{δ V}{δ y}^j - \frac{δ V}{δ z}^k$
Where V=potential energy
$F = - \frac{δ (20 \frac{x y}{z})}{δ x}^i - \frac{δ (20 \frac{x y}{z})}{δ y}^j - \frac{δ (20 \frac{x y}{z})}{δ z}^k$
$F = - \frac{20 y}{z}^i - \frac{20 x}{z}^j + \frac{20 x y}{z^{2}}^k$

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Similar questions

U = \frac{20 x y}{z}

U = \frac{20 x y}{z}

\to E = (4 a x y \sqrt{z})^i + (2 a x^{2} \sqrt{z})^j + (\frac{a x^{2} y}{\sqrt{z}})^k

a

x + y \leq 8 x + 4 y \geq 12 5 x + 8 y = 20 x, y \geq 0

^i,^j,^k

x, y, z

\to u = x^i + y^j + z^k, \to v = y^i + z^j + x^k

\to w = z^i + x^j + y^k

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