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A force vec(F)=(-y hat(i)+ x hat(j))N ac...

A force `vec(F)=(-y hat(i)+ x hat(j))N` acts on a particle as it moves in an anticlockwise circular motion in x-y plane. The centre of the circle is at the origin. If the work done by the force is `32 pi J` in one complete revolution then asSigmaing `x, y` to be in meters, find the radius of the path.

Text Solution

Verified by Experts

The force is perpendicular to the radius vector `vec(R)= x hat(i)+ y hat(j) rArr` Force is tangential
Torque `| tau|=R|vec(R)|=R sqrt(x^(2)+y^(2))=R^(2)`
`W= int_(0)^(theta) tau d theta = R^(2)2 pi`
`R^(2)2 pi = 32 pi rArr R=4 m`
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Knowledge Check

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