A large hemispherical water tank of radius $$R$$ is filled with water initially up to a height $$h=R/2$$. The water starts dripping out through a small orifice of cross section area $$a$$ at its spherical bottom. The time taken to get the tank completely empty, neglecting viscosity, is

A

$$t=\frac{19\pi R^2}{60a}\sqrt{\frac{R}{g}}$$

B

$$t=\frac{3\pi R^2}{10a}\sqrt{\frac{R}{g}}$$

C

$$t=\frac{17\pi R^2}{60a}\sqrt{\frac{R}{g}}$$

D

$$t=\frac{\pi R^2}{4a}\sqrt{\frac{R}{g}}$$