The potential energy function (in J) of a particle in a region of space is given as Here and are in meter. The magnitude of -component of force (in N) acting on the particle at point P(1, 2, 3)m is

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Solution

Q.
The potential energy function (in J) of a particle in a region of space is given as $U = (2 x^{2} + 3 y^{3} + 2 z) .$ Here $x, y$ and $z$ are in meter. The magnitude of $x$ -component of force (in N) acting on the particle at point P(1, 2, 3)m is [2024]

1 2

2 6

3 4

4 8

Ans.
(3)

Given $U = 2 x^{2} + 3 y^{3} + 2 z$

$x$ -component of force, $F_{x} = - \frac{\partial U}{\partial x} = - 4 x$

At $x = 1$ magnitude of $F_{x}$ is 4 N

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