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 4 R . The angle of projection θ is then given by___

Question

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 4 R . The angle of projection θ is then given by___, θ = cos - 1 g T 2 π 2 R 1 2, θ = cos - 1 π 2 R g T 2 1 2, θ = sin - 1 π 2 R g T 2 1 2, θ = sin - 1 2 g T 2 π 2 R 1 2

MARKS App · Accepted Answer

T = 2 π ω = 2 π R v ⇒ v = 2 π R T H = v 2 sin 2 θ 2 g ⇒ 4 R = 4 π 2 R 2 sin 2 θ 2 g T 2 ⇒ sin 2 θ = 2 g T 2 π 2 R ⇒ sin θ = 2 g T 2 π 2 R 1 / 2 ⇒ θ = sin - 1 2 g T 2 π 2 R 1 2

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