# Electrostats + Mechanics = Fun

Classical Mechanics Level 5

You took a Hollow spherical ball and gave it an angular velocity $$\omega = 10\text{ rad/sec}$$ (clockwise) and dropped it from a height $$h = 45.5\text{ m}$$. Above the rough horizontal ground ,In a region of uniform Electric field , $$E = 6 × {10}^{6}\text{ N/C}$$ directed in the horizontal direction (Right).

We observed that after it's collision with the ground it goes to a maximum height of $$2.3\text{ m}$$.

Find the Range of the projectile travelled by the ball's centre of mass in between first and second collision.

Details and Assumptions:

• The ball has a mass $$M = 2\text{ kg}$$ and is uniformly charged $$( q = 3\mu C )$$. Radius of ball $$R = 0.5 \text{ m}$$

• The height measured is of centre of mass of ball from the ground.

• The ball remained in contact with the ground for $$t = {10}^{-6} \text{ sec}$$.

• Coefficient of friction $$\mu = \dfrac{1}{3}$$, take $$g = 10\text{ m/s}^2$$.

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