A) \[\sqrt{{{a}_{1}}\,{{a}_{2}}}\,\,t\]
B) \[\frac{2{{a}_{1}}{{a}_{2}}}{{{a}_{1}}+{{a}_{2}}}\,\,t\]
C) \[\frac{{{a}_{1}}+{{a}_{2}}}{2}\,\,t\]
D) \[\sqrt{2{{a}_{1}}{{a}_{2}}}\,\,t\]
Correct Answer: A
Solution :
\[S=\frac{1}{2}{{a}_{1}}{{t}^{2}}=\frac{1}{2}{{a}_{2}}{{({{t}_{0}}+t)}^{2}}\] \[V\,\,=\,\,(\sqrt{{{a}_{1}}}-\sqrt{{{a}_{2}}})\,\,\times \,\,\sqrt{2s}\] \[\left( \frac{1}{\sqrt{{{a}_{2}}}}-\frac{1}{\sqrt{{{a}_{2}}}} \right)\,\,\times \,\sqrt{2S}\,=\,\,t\] \[\sqrt{2S}\,=\,\frac{\sqrt{{{a}_{1}}}\sqrt{{{a}_{2}}t}}{\sqrt{{{a}_{1}}}\,-\,\sqrt{{{a}_{2}}}}\] \[V\,\,=\,\,\sqrt{{{a}_{1}}{{a}_{2}}t}\]
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