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  • A particle of mass m is acted upon by a force F given by the empirical law  <img alt="F = \frac{R}{t^{2}}\nu (t)" src="https://learn.careers360.com/latex-image/?%5Cdpi%7B100%7D%20F%20

A particle of mass m is acted upon by a force F given by the empirical law  F = \frac{R}{t^{2}}\nu (t).   If this law is to be tested experimentally by observing the motion starting from rest, the best way is to plot :

Option: 1

\nu (t) \, against\, t^{2}


Option: 2

log\, \nu (t) \, against\, \frac{1}{t^{2}}


Option: 3

log\, \nu (t) \, against\, t


Option: 4

log\, \nu (t) \, against\, \frac{1}{t}


Answers (1)

best_answer

\begin{aligned} &F=\frac{R}{t^{2}} v(t)\\ &\Rightarrow m \frac{d v}{d t}=\frac{R}{t^{2}} v(t)\\ &\Rightarrow \int \frac{d v}{v}=\int \frac{R d t}{m t^{2}}\\ &\ln v=-\frac{R}{m t}\\ &\Rightarrow \ln v \propto \frac{1}{t} \end{aligned}

\\ So, the \ plot \ of \ log v(t)$ \ against \ $\frac{1}{t}$ will be a straight line.Thus plotting will be most convenient.

Posted by

Sanket Gandhi

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