The quantities which have the same dimensions as those of solid angle are [2024]

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Solution

Q.
The quantities which have the same dimensions as those of solid angle are [2024]

1 strain and angle

2 stress and angle

3 strain and arc

4 angular speed and stress

Ans.
(1)

Solid angle is the ratio of area to the square of perpendicular distance.

$Ω = \frac{S}{r^{2}} = \frac{M^{0} L^{2} T^{0}}{M^{0} L^{2} T^{0}} = [M^{0} L^{0} T^{0}]$

Strain $= \frac{Δ L}{L} = \frac{M^{0} L^{1} T^{0}}{M^{0} L^{1} T^{0}} = [M^{0} L^{0} T^{0}]$

Angle = $= \frac{Arc}{Length} = \frac{M^{0} L^{1} T^{0}}{M^{0} L^{1} T^{0}} = [M^{0} L^{0} T^{0}]$

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