A) \[\frac{2{{a}_{1}}{{a}_{2}}}{{{a}_{1}}+{{a}_{2}}}t\]
B) \[\sqrt{2{{a}_{1}}{{a}_{2}}}t\]
C) \[\sqrt{{{a}_{1}}{{a}_{2}}t}\]
D) \[\frac{{{a}_{1}}+{{a}_{2}}}{2}t\]
Correct Answer: C
Solution :
| \[\sqrt{\frac{2\ell }{{{a}_{2}}}}-\sqrt{\frac{2\ell }{{{a}_{1}}}}=t\] |
| \[\Rightarrow \]\[\frac{\sqrt{2\ell }}{t}=\frac{\sqrt{{{a}_{1}}{{a}_{2}}}}{\sqrt{{{a}_{1}}}-\sqrt{{{a}_{2}}}}\] |
| \[\sqrt{2{{a}_{1}}\ell }-\sqrt{2{{a}_{2}}\ell }=v\] |
| \[\Rightarrow \] \[\frac{\sqrt{2\ell }}{v}=\frac{1}{\sqrt{a{{ & }_{1}}}-\sqrt{{{a}_{2}}}}\]\[\Rightarrow \]\[\frac{v}{t}=\sqrt{{{a}_{1}}{{a}_{2}}}\]\[\Rightarrow \]\[v=\left( \sqrt{{{a}_{1}}{{a}_{2}}} \right)t.\] |
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