A particle of mass m is moving along the x -axis with initial velocity u i. It collides elastically with a particle of mass 10 m at rest and then…

A particle of mass $\displaystyle m$ is moving along the $\displaystyle x$-axis with initial velocity $\displaystyle \mathrm{u} \hat{i}$. It collides elastically with a particle of mass $\displaystyle 10$ m at rest and then moves with half its initial kinetic energy (see figure). If $\displaystyle \sin \theta_1=\sqrt{\mathrm{n}} \sin \theta_2$ then value of n is \_\_\_\_.