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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 |
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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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