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Q.

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

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a

4 s

b

3 s

c

1 s

d

2 s

answer is B.

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Detailed Solution

$\begin{array}{l} F_{x} = - \frac{d U}{d x} = \frac{d}{d x} (6 x + 8 y) = - 6 \\ F_{y} = - \frac{d U}{d y} = - 8 \\ a_{x} = \frac{6}{2} = 3, a_{y} = \frac{8}{2} = 4 \end{array}$
after time $(t) x = x_{0} - \frac{1}{2} a_{x} t^{2} = 6 - \frac{1}{2} \times 3 \times t^{2}$
$y = y_{0} - \frac{1}{2} a_{y} t^{2} = 4 - 2 t^{2}$
body crosses y axis at x = 0
$6 - \frac{3}{2} t^{2} = 0, t = 2 \sec$

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