A particle of mass m is projected with velocity u at an angle $\alpha$ with horizontal. During the period when particle decends from highest point to the position where its velocity vector makes $\alpha/2$ angle with horizontal, work done by gravity force is

Question

$$(a)\;\frac{1}{2} mu^2\tan ^2 \alpha \quad (b)\;\frac{1}{2} mu^2 \cos ^2 \alpha  \tan ^2 \alpha/2 \quad (c)\;\frac{1}{2} mu^2 \tan ^2  \alpha/2 \quad (d)\;\frac{1}{2} mu^2 \cos ^2 \alpha/2 m^2 \alpha$$