A force F ⁡ → = - K ⁡ y ⁡ i ^ + x ⁡ j ^ (where K is a positive constant) acts on a particle moving in the x - y plane. Starting from the origin, the particle is taken along the positive x -axis to the point ( a , 0 ) and then parallel to the y -axis to the ( a , a ) . The total work done by the force F ⁡ → on the particle is

Question

A force F ⁡ → = - K ⁡ y ⁡ i ^ + x ⁡ j ^ (where K is a positive constant) acts on a particle moving in the x - y plane. Starting from the origin, the particle is taken along the positive x -axis to the point ( a , 0 ) and then parallel to the y -axis to the ( a , a ) . The total work done by the force F ⁡ → on the particle is, - 2 K a 2, 2 K a 2, - K a 2, K a 2

MARKS App · Accepted Answer

F = - K y i ^ + x j ^ On moving from origin to (a, 0). Work done = ∫ 0 a - K y i ^ + x j ^ . dx = 0 as y = 0 Work done from (a, 0) to (a, 0) Work done w = ∫ 0 a - K y i ^ + x j ^ dy but x = a = ∫ 0 a - K a dy = - Ka 2

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