Kelvi

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

hard

Motion in a Plane

2021

physics

$\theta = \cos^{-1} \left( \frac{gT^2}{\pi^2 R} \right)^{\frac{1}{2}}$

Explanation

To solve this problem, we need to analyze the motion of the particle in two scenarios: circular motion and projectile motion. $\\$ 1. Circular Motion: $\\$ • The particle moves in a circle of radius $R$ with uniform speed. $\\$ • Time taken to complete one revolution is $T. \\$ The speed $v$

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