A particle of mass 1 kg is projected at t =0 from a point ' O ' on the ground with a speed 'u' at an angle 45° to the horizontal. The magnitude of…

A particle of mass $\displaystyle 1$ kg is projected at $\displaystyle \mathrm{t}=0$ from a point ' O ' on the ground with a speed 'u' at an angle $\displaystyle 45$° to the horizontal. The magnitude of angular momentum of the particle about ' O ' at time $\displaystyle \frac{\mathrm{u}}{\mathrm{g}}$ is given by $\displaystyle \frac{7 u^3}{a g}$. Then the value of $\displaystyle a$ is \_\_\_\_. (Take $\displaystyle \frac{1}{\sqrt{2}}=0.7$ and $\displaystyle g=10 \mathrm{~m} / \mathrm{s}^2$ )