A particle moving horizontally with a velocity u strikes a fixed frictionless sphere at a height R/2 above the center of sphere. After striking the sphere, velocity of particle changes to vertically upward .If R be the radius of sphere, the maximum height attained by the particle with respect to center of sphere is

• A

  $\frac{{\mathrm{u}}^2}{6\mathrm{g}}+\frac{\mathrm{R}}{2}$

• B

  $\frac{{\mathrm{u}}^2}{2\mathrm{g}}+\frac{\mathrm{R}}{2}$

• C

  $\frac{{\mathrm{u}}^2}{3\mathrm{g}}+\frac{\mathrm{R}}{2}$

• D

  $\frac{{\mathrm{u}}^2}{4\mathrm{g}}+\frac{\mathrm{R}}{2}$