Question

The angular diameter of sun is 1920s If the distance of the sun from the earth is 1.5 × 10¹¹ m, what is the linear diameter of the sun ?
(a) 1.4 x 10⁹ m
(b) 14.0 x 10⁹m
(c) 1.4 x 10¹⁰ m
(d) 1.4 x 10⁸m

*WHOEVER ANS. IT FIRST AND CORRECT I'LL MARK HIM BRAINLIEST*​

Answer 1

Explanation:

It is given that the

Angular diameter of the sun, θ=1920′′

The distance between the sun and the earth, l=1.5×1011m

First let us convert the angular diameter from the seconds into the minutes . 1min=60sec

1′′=160′

Substitute the above relation for the given angular diameter, we get

1920′′=192060

By performing division in the right hand side of the equation, we get

θ=32′

Next, let us convert the minutes into the degrees. 1min=160∘ .

32′=3260∘=0.53∘

Let us convert the degree into the radian, we get

1∘=π180rad

0.53∘=0.53∘×π180=0.009rad

Hence the angular diameter is obtained as 0.009rad .

Let us use the formula of the linear diameter of the sun, we get

d=lθ

Substituting the known parameters in the above formula, we get

d=1.5×1011×0.009

By performing various basic arithmetic operations, we get

d=1.4×109m

Hence the linear diameter of the sun is obtained as 1.4×109m