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The potential energy of a body of mass m is given by U = ax + by, where x and y are the position coordinates of the particle. The acceleratio of the particle is

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$\frac{{(a + b)}^{\frac{1}{2}}}{m}$

$\frac{a^{2} + b^{2}}{m}$

$\frac{\sqrt{a^{2} + b^{2}}}{m}$

$\frac{a + b}{m}$

answer is D.

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Detailed Solution

For a conservative system $F = - \frac{d U}{d r} = - (\frac{\partial U}{\partial x}) \hat{i} - (\frac{\partial U}{\partial y}) \hat{j}$

$\overset{⇀}{F} = - \hat{i} a - \hat{j} b |\overset{⇀}{F}| = \sqrt{a^{2} + b^{2}} a c c e l e r a t i o n = \frac{\sqrt{a^{2} + b^{2}}}{m}$

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