A force F = x 2 y 2 i + x 2 y 2 j (N) acts on a particle wh…

Physics Work, Energy, Power and Collision Conservative and Nonconservative Forces and Equilibrium MCQ (Single Correct)

A force F = x 2 y 2 i + x 2 y 2 j (N) acts on a particle which moves in the XY plane.

Determine F is conservative or not and

find the work done by F as it moves the particle from A to C (fig.) along each of the path’s ABC, ADC, and AC.

Text Solution

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The correct answer is:

CHECK THE SOLUTION.

W ABC = W ADC = (J), W AC = (J)]

Sol. w =

which is not a perfect integral and hence cannot be integrated without knowing y = f(x) or x = f(y). So,

work done by depends on path. So, it is non–conservative force.

While moving along AB, y = 0 and along BC, x = a.

W ABC =

= 0 + a 2 × =

While moving along AD, x = 0 and along DC, y = a

So W ADC =

= 0 + a 2 . =

Along AC

x = y

So, W AC =

= = .

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