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A particle goes along a quadrant of a ci...

A particle goes along a quadrant of a circle of radius 10m from A to B as shown in fig. Find the magnitude of displacement and distance along the path AB, and angle between displacement vector and x-axis ?

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Displacement `vec(AB) = vec(OB) - vec(OA) = (10hatj - 10 hati)` m
`" "|vec(AB)| = sqrt(10^(2) + 10^(2)) = 10 sqrt2 `m
From `Delta OBC tantheta = (OA)/(OB) = (10)/(10) =1 rArr theta = 45^(@)`
Angle between displacement vector `vec(OC)` and x-axis = `90^(@) + 45^(@)= 135^(@)`
Distance of path AB = `(1)/(4)` (circumference) = `(1)/(4)(2 pi R) m = (5pi) m`
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