The distance of the Sun from earth is 1.5 × 10¹¹ m and its angular diameter is (2000) s when observed from the earth. The diameter of the Sun will be :

Solution

Physics sir · 3 steps

The Sun is so far away that its diameter is just an arc: turn 2000 seconds into radians and use D = rθ.

1. Small angle as arc. The angle is tiny, so the Sun's diameter is almost exactly an arc of a circle centred on the earth. Arc length equals radius times angle, with the angle in radians.
2. Seconds to radians. One second of arc is 1/3600 of a degree, so 1'' = π/(180 × 3600) rad = 4.848 × 10⁻⁶ rad. Then 2000'' = 2000 × 4.848 × 10⁻⁶ = 9.70 × 10⁻³ rad.

   D = rθ = (1.5 × 10¹¹ m) × (9.70 × 10⁻³) ≈ 1.45 × 10⁹ m

3. So. The diameter of the Sun is about 1.45 × 10⁹ m, which is option (c).

The idea to keep. For anything far away, size equals distance times angle. Always convert the angle to radians first: 1'' ≈ 4.85 × 10⁻⁶ rad.

Answer from the NTA final answer key. Solution by PrepWiser.