- Home
- Standard 11
- Physics
4-1.Newton's Laws of Motion
hard
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
A
$log\, v(t)$ against $\frac{1}{t}$
B
$v(t)$ against $t^2$
C
$log\, v(t)$ against $\frac{1}{t^2}$
D
$v(t)$ against $t$
(JEE MAIN-2016)
Solution
$\begin{array}{l}
From\,F = \frac{R}{{{t^2}}}v\left( t \right) \Rightarrow m\frac{{dv}}{{dt}} = \frac{R}{{{t^2}}}v\left( t \right)\\
Integrating\,both\,sides\,\int {\frac{{dv}}{v} = \int {\frac{{Rdt}}{{m{t^2}}}} } \\
In\,v = – \frac{R}{{mt}}\\
\therefore \,In\,v\, \propto \frac{1}{t}
\end{array}$
Standard 11
Physics
