A) log v(t) against t
B) v(t) against \[{{t}^{2}}\]
C) log v(t) against\[\frac{1}{{{t}^{2}}}\]
D) log v(t) against \[\frac{1}{t}\]
Correct Answer: D
Solution :
| [d] \[m\frac{dV}{dt}=\frac{R}{{{t}^{2}}}V\] |
| \[\Rightarrow m\frac{dv}{v}=R\frac{dt}{{{t}^{2}}}\] |
| \[\Rightarrow \int\limits_{{{V}_{1}}}^{{{V}_{2}}}{\frac{dV}{V}}=R\int\limits_{{{t}_{1}}}^{{{t}_{2}}}{\frac{dt}{{{t}^{2}}}}\] |
| \[\left. \Rightarrow \ell n\left( \frac{{{V}_{2}}}{{{V}_{1}}} \right)=\frac{-R}{t} \right|_{{{t}_{1}}}^{{{t}_{2}}}\] |
| \[\Rightarrow m\ell n\left( \frac{{{V}_{2}}}{{{V}_{1}}} \right)=\frac{-R}{t}\left( \frac{1}{{{t}_{2}}}-\frac{1}{{{t}_{2}}} \right)\] |
| \[\log V\,\,vs\,\,\frac{1}{t}\] will be a st. line curve |
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