Dimensional expression of solid angle is
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Solid angle is defined as, R^2 * ∆(s.a.) = ∆(area subtended) So, ∆(s.a.) = ∆(area subtended)/R^2 Which means, ∆(s.a.) has a dimesnion of L^2/L^2, which equals L^0 Hence, it is dimensionless.
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