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The potential energy (in joule) of a body of mass 2kg moving in the XY-plane is given by U = 6x + 8y, where x and y are in meters. If the body is at rest at point (6m, 4m) at time t = 0, it will cross y-axis at time t equal to.

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$\sqrt{2} s$

answer is B.

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Detailed Solution

$F_{x} = - \frac{\partial U}{\partial x} = - 6$

and

$F_{y} = - \frac{\partial U}{\partial y} = - 8$

Now, $F_{x} = {ma}_{x} \Rightarrow a_{x} = \frac{- 6}{2} = - 3 m / s^{2}$

When it will cross y − axis at that time x will be zero

Using, $x = ut + \frac{1}{2} a_{x} t^{2}$

$0 - 6 = 0 - \frac{1}{2} \times 3 \times t^{2}$

$t = 2 s$

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