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Question

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

A
4ka2
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B
2ka2
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C
2ka2
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D
4ka2
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Solution

The correct option is C 2ka2
For an infinitesimally small displacement dr ,
Work done by F will be, dW=F.drdW=2k [y^i+x^j].[dx^i+dy^j]dW=2k[ydx+xdy]=2k d[xy]
Now, integrating within limits,

W0dW=2k(a,a)(0,0)d(xy)W=2k[xy]a,a0,0=2ka2

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