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Question

A particle of mass m moves along the quarter section of the circular path whose centre is at the origin. The radius of the circular path is a. A force F=y^ix^j N acts on the particle, where x,y denote the coordinates of position of the particle. Calculate the work done by this force, if the particle displaces from point A(a,0) to point B(0,a) along the circular path.

A
π a24 J
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B
π a22 J
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C
π a22 J
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D
π a24 J
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Solution

The correct option is C π a22 J
Work done by variable force is W=F.dr
W=F.(dx^i+dy^j+dz^k)
W=Fxdx+Fydy=ydxxdy

Equation of circle passing through point A, point B with centre origin is x2+y2=a2
As x,y points lie on the circle, we can substitute
x=acosθ,y=asinθ,
dx=asinθ dθ,dy=acosθ dθ



W=a2sin2θ dθa2cos2θ dθ
W=a2dθ
As particle moves from A to B, θ varies from 0 to 90
W=a2π/20dθ

W=π a22J

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