The distance of the sun from earth is `1.496xx10^(11)m.` If the angular diameter of the sun is 2000'', find the diameter of the sun.

Options

A. `2.45 xx 10^(10)m`
B. `1.45xx10^(10)m`
C. `1.45xx10^(9)m`
D. `0.14xx10^(9)`m

Answer

C

Explanation

1 min = 60 s
`1^(@)= 60 min `
`1^(@) = 3600` sec
`2000 s =1/3600 xx 2000` degree
`20/36` degree = `pi/180 xx 20/36` rad
`D = r^(theta) = 1.5 xx 10^(11) xx pi/180 xx 20/36`
`= (1.5 pi)/(18^(2)) xx 10^(11)`
`= 0.0145 xx 10^(11)`
`= 1.45 xx 10^(9)`