1.

How much time does the minute hand of a watch take to describe an angle of \(\dfrac{3\pi}{2}\) radian?1. 30 minutes2. 45 minutes3. 15 minutes4. 20 minutes

Answer» Correct Answer - Option 2 : 45 minutes

Given: 

The angle described by the minute hand is 3π/2 radian

Concept used:

Minute hand will make 360° in 60 minutes 

And, π radian is equal to 180° 

Calculation:

3π/2 radian = (3 × 180°)/2 = 270° 

Now, Minute hand will make 360° in 60 minutes 

Minute hand will make 1° in 60/360 minutes 

Minute hand will make 270° in 60/360° × 270° minutes 

⇒ 270°/6° 

⇒ 45 minutes 

∴ The minute hand will describe 3π/2 radian in 45 minutes



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