The distance of the Sun from earth is $$1.5 \times 10^{11}$$ m and its angular diameter is $$2000''$$ when observed from the earth. The diameter of the Sun will be

We are given that the distance of the Sun from Earth is $$R = 1.5 \times 10^{11}$$ m and its angular diameter is $$\theta = 2000''$$ (arc-seconds).

Convert angular diameter to radians.

We know that $$1'' = \frac{1}{206265}$$ rad.

$$\theta = 2000'' = \frac{2000}{206265} \approx 9.7 \times 10^{-3}$$ rad

Calculate the diameter of the Sun.

For small angles, the diameter $$D$$ is related to distance $$R$$ and angular diameter $$\theta$$ by:

$$D = R \times \theta$$

$$D = 1.5 \times 10^{11} \times 9.7 \times 10^{-3}$$

$$D = 1.45 \times 10^{9}$$ m

Therefore, the diameter of the Sun is $$1.45 \times 10^{9}$$ m.

The correct answer is Option C.