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

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

Options

G1 Physics · Accepted Answer

Step 1: Circular speed is v=2πR/T. Step 2: Projectile maximum height is H=v²sin²θ/(2g). Step 3: Given H=4R: [4π²R²/T²]sin²θ/(2g)=4R. Step 4: Therefore sin²θ=2gT²/(π²R), so θ=sin⁻¹√[2gT²/(π²R)]. Final answer: D.