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Physics · UNITS AND MEASUREMENT
हिन्दीA spherical surface area element \( dA = 0.25\text{ m}^2 \) at a distance \( r = 0.5\text{ m} \) from the center subtends a solid angle \( \Omega \). An arc of length \( ds = 0.2\text{ m} \) on a circle of the same radius \( r = 0.5\text{ m} \) subtends a plane angle \( \theta \). The ratio of the numerical value of \( \Omega \) (in steradians) to \( \theta \) (in radians) is:
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Correct answer · Option A
\( 2.5 \)
Explanation
Solid angle \( \Omega = \frac{dA}{r^2} = \frac{0.25}{0.5^2} = 1\text{ sr} \). Plane angle \( \theta = \frac{ds}{r} = \frac{0.2}{0.5} = 0.4\text{ rad} \). The ratio \( \frac{\Omega}{\theta} = \frac{1}{0.4} = 2.5 \).
