A) \[2\,\pm \,\sqrt{6}\]
B) \[\sqrt{2}\]
C) \[2+\sqrt{2}\]
D) \[2+\sqrt{6}\]
Correct Answer: B
Solution :
Let \[AB=x\] \[\therefore \] \[OA=2x\] and time taken by the body to cover the distance OA and AB are \[{{t}_{1}}\] and \[{{t}_{2}}\] respectively. Then, \[2x=0+\frac{1}{2}gt_{1}^{2}\] \[[\because \,\,u=0]\] \[\Rightarrow \] \[4x=gt_{1}^{2}\] and \[x=0+\frac{1}{2}gt_{2}^{2}\] \[\Rightarrow \] \[2x=gt_{2}^{2}\] \[\therefore \] Required ratio \[=\frac{{{t}_{1}}}{{{t}_{2}}}=\frac{\sqrt{\begin{matrix} 4x \\ g \\ \end{matrix}}}{\sqrt{\begin{matrix} 2x \\ g \\ \end{matrix}}}\] \[\Rightarrow \] \[\frac{{{t}_{1}}}{{{t}_{2}}}=\frac{\sqrt{2}}{1}\]
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