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Name dimensionlesss physical quantity an...

Name dimensionlesss physical quantity and show that it is dimensionless.

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Angle is a dimensionless quantity.
As per definition the angle subtended at the centre of a circle by an arc has the value equal to the ratio of the arc and the radius of the circle.
Thus angle = `("arc")/("radius")`. Arc and radius both denote lengths. Hence dimension of angle = `(L)/(L) = L^(1-1) = L^(0) = 1`.
Hence angle is a dimensionless quantity.
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