A particle of mass m is dropped from a height h above the ground. At the same time another particle of the same mass is thrown vertically upwards from the ground with a speed of \(\sqrt{2\text{gh}}\). If they collide head-on completely inelastically, the time taken for the combined mass to reach the ground, in units of \(\sqrt{\frac{\text{h}}{\text{g}}} \) is :

1
\(\frac{1}{2}\)
2
\(\sqrt{\frac{3}{2}} \)
3
\(\sqrt{\frac{3}{4}} \)
4
\(\sqrt{\frac{1}{2}} \)

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