At the highest point, the vertical component of the velocity becomes zero, and only the horizontal component \( u_x = u \cos 45^\circ = \frac{u}{\sqrt{2}} \) remains.
The maximum height \( h \) reached by the body is given by:
\[ h = \frac{(u \sin 45^\circ)^2}{2g} = \frac{\left(\frac{u}{\sqrt{2}}\right)^2}{2g} = \frac{u^2}{4g}. \]The angular momentum \( L \) about the point of projection at the highest point is:
\[ L = m \cdot u_x \cdot h = m \cdot \frac{u}{\sqrt{2}} \cdot \frac{u^2}{4g} = \frac{\sqrt{2}mu^3}{8g}. \]Thus, the value of \( X \) is:
\[ X = 8. \]Statement-1: \( \text{ClF}_3 \) has 3 possible structures.
Statement-2: \( \text{III} \) is the most stable structure due to least lone pair-bond pair (lp-bp) repulsion.
Which of the following options is correct?
The largest $ n \in \mathbb{N} $ such that $ 3^n $ divides 50! is: