A particle moving in a circle of radius R with a uniform speed takes a time T to complete one revolution. If this particle were projected with the same speed at an angle ' θ ' to the horizontal, the maximum height attained by it equals 4R. The angle of projection. θ, is then given by:
A particle moving in a circle of radius R with a uniform speed takes a time T to complete one revolution. If this particle were projected with the same speed at an angle ' θ ' to the horizontal, the maximum height attained by it equals 4R. The angle of projection. θ, is then given by:
Option 1 -
θ = cos⁻¹ (gT²/π²R)¹ᐟ²
Option 2 -
θ = cos⁻¹ (π²R/gT²)¹ᐟ²
Option 3 -
θ = sin⁻¹ (π²R/gT²)¹ᐟ²
Option 4 -
θ = sin⁻¹ (2gT²/π²R)¹ᐟ²
Asked by Shiksha User
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1 Answer
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Correct Option - 4
Detailed Solution:T = 2πR/v ⇒ v = 2πR/T
H? = (v²sin²θ)/2g = (2π²R²sinθ)/ (gT²) = 4R
sinθ = (2gT²)/ (π²R)¹/²
θ = sin? ¹ [ (2gT²)/ (π²R)]¹/²
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