A) \[{{h}_{1}}:{{h}_{2}}\]
B) \[{{h}_{2}}/{{h}_{1}}\]
C) \[{{\sqrt{h}}_{1}}:\sqrt{{{h}_{2}}}\]
D) \[{{h}^{2}}_{1}:{{h}^{2}}_{2}\]
Correct Answer: C
Solution :
Distance fallen by a freely body, \[\Rightarrow \] \[s=\frac{1}{2}g{{t}^{2}}\] \[s\propto {{t}^{2}}\] ? [\[\because \frac{1}{2}g\]is constant] \[\therefore \] \[\frac{{{s}_{1}}}{{{s}_{2}}}=\frac{t_{1}^{2}}{t_{2}^{2}}\] \[\Rightarrow \] \[\frac{{{h}_{1}}}{{{h}_{2}}}=\frac{t_{1}^{2}}{t_{2}^{2}}\] \[\Rightarrow \] \[\frac{{{t}_{1}}}{{{t}_{2}}}=\sqrt{\frac{{{h}_{1}}}{{{h}_{2}}}}\]
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