• # question_answer A particle of mass m is acted upon by a force F given by the empirical law $F=\frac{R}{{{t}^{2}}}V(t)$.If this law is to be tested experimentally by observing the motion starting from rest, the best way is to plot:    [JEE ONLINE 10-04-2016] 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 $\frac{1}{t}$

 [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