QJEEM16Ph4d96: JEE Main 2016 Physics - Class 11 JEEM16Ph4d96 Solution: A particle of mass m is acted upon by a force F given by the…

Question

Verified Solution • 2025–26 Session moderate

A particle of mass m is acted upon by a force F given by the empirical law F =

{R \over {{t^2}}}\,v\left( t \right).

If this law is to be tested experimentally by observing the motion starting from rest, the best way is to plot :

Accepted Answer

Given,

F =

{R \over {{t^2}}}

v(t)

\Rightarrow

m

{{dv} \over {dt}}

=

{R \over {{t^2}}}

(v)

\Rightarrow

{{dv} \over v}

=

{R \over m}

{{dt} \over {{t^2}}}

Intergrating both sides,

\int {{{dv} \over v} = {R \over m}\int {{{dt} \over {{t^2}}}} }

\Rightarrow

lnv =

{{R \over m}}

\times

\left( { - {1 \over t}} \right)

+ C

\Rightarrow

lnv =

-

{{R \over m}}

\left( {{1 \over t}} \right)

+ C

Graph between lnv and

{{1 \over t}}

will be straight line curve.

Step-by-Step Verified Solution