A) variable
B) \[\sqrt{\frac{2a}{b}}\]
C) \[\frac{a}{2b}\]
D) \[\sqrt{\frac{a}{2b}}\]
Correct Answer: D
Solution :
\[\operatorname{y}=b{{x}^{2}}\] \[\frac{dy}{dt}=2bx.\frac{dx}{dt}\Rightarrow \frac{{{d}^{2}}y}{d{{x}^{2}}}=2b{{\left( \frac{dx}{dt} \right)}^{2}}+2bx\,\frac{{{d}^{2}}x}{d{{t}^{2}}}\] \[\operatorname{a}=2b{{v}^{2}}+0\,\,\,\Rightarrow \,\,\,v=\sqrt{\frac{a}{2b}}\]
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