Question

The angle of 1′ (minute of arc) in radian is nearly equal to

(1) 1.75 × 10^–2 rad

(2) 2.91 × 10^–4 rad

(3) 4.85 × 10^–4 rad

(4) 4.80 × 10^–6 rad

Answer 1

Answer - (2) 2.91 × 10^-4

 

Solution - 

1° = 60' 

1' = (1/60)° —(1)

1° = (π/180) rad

from (1)

(1/60)° = (1/60)° ×  (π/180) rad

            = (π/10800) rad

            = 2.91 × 10^-4 rad

Comments

This ans is wrong
Because in one minute contain 6 degree.
And you said in 1 drgree contain 60 minutes.
Specify proper ans.

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answer and solution both are correct

I think you are confusing the unit of measure minute.

If you take minute to be the unit of time then the first result holds wherein 1 degree = 4 minute.

This is easy to calculate too:

There are 24 hours in one day and 60 minutes in one hour, equalling 24*60 = 1440 minutes in a day.

Now, you may know the fact that Earth has different timezones depending on the longitude that they lie on. These are measured starting from the Greenwich meridian and extend to +180° and -180° in the two directions of East and West respectively. This totals to 360°.

Now to calculate the time difference between two longitude separated by 1° is done by dividing the total number of minutes in a day, by the total angle covered in a day. i. e.

1440/360 = 4 minutes.

Now for the other minute.

The angular measure of degree can be sub divided into smaller parts known as minute, and the relationship that holds is:

1° = 60' = 60 minutes.

(Fun fact)
Another thing that can be derived from this is:

1° = 60 minutes(') = 4 minutes.

i. e. 15 minutes(') = 1 minute.

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its correct by the way verified by aakashian

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Send right answer

Answer 2

b) 2.91 X 10–⁴ radian