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Byju's Answer

Standard XII

Physics

Potential Energy

The potential...

Question

The potential energy of a particle of mass 1 kg moving in the X-Y plane obeys the law $ϕ = 3 x + 4 y J$ where x and y are in meters. If the particle is at rest at (6m, 8m) at time t = 0, the work done by conservative force on the particle from the initial position to the instant when it crosses the x-axis is

25 J

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- 25 J

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50 J

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- 50 J

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Solution

The correct option is C 50 J
$F = - 3^i - 4^j$ . This force is directed towards the origin from the point (6, 8) as the slopes of the line joining the point and the origin and the direction of the force are same. The particle will cross the x-axis at the origin. Work done by conservative forces $W_{c f} = U_{i} - U_{f} = (3 \times 6 + 4 \times 8) - 0 = 50 J$

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