The suns angular diameter is measured to be 1920". The distance of the sun from the earth is 1.496 × 1011 m. What is the diameter of the sun ?

Question

The suns angular diameter is measured to be 1920". The distance of the sun from the earth is 1.496 × 1011 m. What is the diameter of the sun ? (A) 1.39 × 109 m (B) 1.39 × 1010 m (C) 1.39 × 1011 m (D) 1.39 × 1012 m

Tardigrade Admin · Accepted Answer

Here,
Distance of the sun from the earth,

d = 1.496 \times 1 0^{11} m

Suns angular diameter,

α = 19 2^{''}

∵ 1^{''} = 4.85 \times 1 0^{- 6} r a d

∴ α = 1920 \times 4.85 \times 1 0^{- 6} r a d

= 9.31 \times 1 0^{- 6} r a d

Suns diameter,

D = α d

D = (9.31 \times 1 0^{- 3}) (1.496 \times 1 0^{11}) m

= 1.39 \times 1 0^{9} m

Q. The suns angular diameter is measured to be $1920$ ". The distance of the sun from the earth is $1.496 \times 1 0^{11} m$ . What is the diameter of the sun ?

$1.39 \times 1 0^{9} m$

$1.39 \times 1 0^{10} m$

$1.39 \times 1 0^{11} m$

$1.39 \times 1 0^{12} m$

Q. The suns angular diameter is measured to be 1920". The distance of the sun from the earth is 1.496×1011m. What is the diameter of the sun ?

1.39×109m

1.39×1010m

1.39×1011m

1.39×1012m

Here, Distance of the sun from the earth, d=1.496×1011m Suns angular diameter, α=192′′ ∵1′′=4.85×10−6rad ∴α=1920×4.85×10−6rad =9.31×10−6rad Suns diameter, D=αd D=(9.31×10−3)(1.496×1011)m =1.39×109m

Q. The suns angular diameter is measured to be $1920$ ". The distance of the sun from the earth is $1.496 \times 1 0^{11} m$ . What is the diameter of the sun ?

$1.39 \times 1 0^{9} m$

$1.39 \times 1 0^{10} m$

$1.39 \times 1 0^{11} m$

$1.39 \times 1 0^{12} m$