# Too much radius, not enough circle

**Classical Mechanics**Level 4

A particle of mass 'm' starts performing circular motion on a vertical plane when given a an horizontal velocity **U** at the lowest point..

This Particle is held by a string of **radius r** which is fixed from one end. The fixed end is at a **height 2r** from the ground.

After completing the circle**7** times, the particle gets released at an angle \(\theta\) above the horizontal in which the fixed end is present, The particle then performs a projectile motion where the **Max height from the ground is 51r/13**, and the **max height from the point of projection is r**.

The particle hits the ground with a** velocity 50m/s, making an angle of 60 degree with the vertical**

Find the minimum length of the string required for this phenomenon to occur. Also find U. And find \(sin \theta\)

**Give your answer in the form \(sin\theta\) +|U| + r**

*Assumptions:*
Take g=10m/s^2
Neglect air resistance.
Round off your 'r' to no decimal places.