A) \[\sqrt{2}\]
B) \[\frac{1}{\sqrt{2}}\]
C) \[\sqrt{2}-1\]
D) \[\frac{1}{\sqrt{2}-1}\]
Correct Answer: C
Solution :
Time taken for the level to fall from H to \[H'\] \[t=\frac{A}{{{A}_{0}}}\sqrt{\frac{2}{g}}\,\,\left[ \sqrt{H}-\sqrt{H'} \right]\] According to problem- the time taken for the level to fall from h to \[\frac{h}{2}\] \[{{t}_{1}}=\frac{A}{{{A}_{0}}}\sqrt{\frac{2}{g}}\ \ \left[ \sqrt{h}-\sqrt{\frac{h}{2}} \right]\] and similarly time taken for the level to fall from \[\frac{h}{2}\] to zero \[{{t}_{2}}=\frac{A}{{{A}_{0}}}\sqrt{\frac{2}{g}}\ \left[ \sqrt{\frac{h}{2}}-0 \right]\] \[\therefore \ \frac{{{t}_{1}}}{{{t}_{2}}}=\frac{1-\frac{1}{\sqrt{2}}}{\frac{1}{\sqrt{2}}-0}=\sqrt{2}-1.\]
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