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A particle is dropped from a certain height. The time taken by it to fall through successive distances of \( 1 \mathrm{~km} \) each will be :
(1) all equal, being equal to \( \sqrt{\frac{2}{g}} \) second.
(2) in the ratio of the square roots of the integers \( 1: \sqrt{2}: \sqrt{3} \)
(3) in the ratio of the difference in the square roots of the integers, i.e.,
\( \sqrt{1},,(\sqrt{2}-\sqrt{1}),(\sqrt{3}-\sqrt{2}),(\sqrt{4}-\sqrt{3}) \ldots \ldots \)
(4) in the ratio of the reciprocals of the square roots
of the integers, ie., \( \frac{1}{\sqrt{1}}, \frac{1}{\sqrt{2}}, \frac{1}{\sqrt{3}} \ldots \).
\( \mathrm{P} \)
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