A uniform rod of mass \(m\) and length \(l\) is placed vertically on the smooth horizontal floor. Now the rod is given a slight push so that it starts falling.

Find the Normal Reaction that the ground applies on it as a function of angle \(\theta\) that the rod makes with the horizontal.

Your answer can be represented as

\(\large{N (\theta) = \frac{mg [a {(\sin\theta - 1)}^{b} + c]}{{( d - e{(\sin\theta)}^{2})}^{f}}} \)

Enter your answer as \( a + b + c + d + e + f \)

**Details and assumptions**:

\( 0 < \theta < \dfrac{\pi}{2} \).

There is no friction between the contact surfaces.

Neglect air dra .

Calculate the Normal reaction before the collision takes place.

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