A particle moving in a circle of radius R with uniform speed takes time T to complete one revolution. If this particle is projected with the same speed at an angle θ to the horizontal, the maximum height attained by it is equal to 4 R . The angle of projection θ is then given by :

Question

A particle moving in a circle of radius R with uniform speed takes time T to complete one revolution. If this particle is projected with the same speed at an angle θ to the horizontal, the maximum height attained by it is equal to 4 R . The angle of projection θ is then given by :, sin − 1 2 g T 2 π 2 R 1 2, sin − 1 π 2 R 2 g T 2 1 2, cos − 1 2 g T 2 π 2 R 1 2, cos − 1 π R 2 g T 2 1 2

MARKS App · Accepted Answer

Time period of circular motion is given by, 2 π R v = T ⇒ v = 2 π R T Now, maximum height H = v 2 sin 2 θ 2 g ⇒ 4 R = 4 π 2 R 2 T 2 sin 2 θ 2 g ⇒ sin θ = 2 g T 2 π 2 R ⇒ θ = sin − 1 2 g T 2 π 2 R 1 2

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