A particle of mass m is acted upon by a force F given by the emprical law `F=(R)/(t^2)upsilon(t)`
If this law is to be tested experimentally by observing the motion starting from rest, the best way is to plot :

Options

A. v(t) against `t^(2)`
B. log v(t) against `(1)/(t^(2))`
C. log v(t) against t
D. log v(t) against `(1)/(t)`

Answer

D

Explanation

`F=(R )/(t_(2))v(t)`
`m(dv)/(dt)=(R )/(t^(2))v(t)`
`int(dv)/(v)=(R )/(m)int(1)/(t^(2))dt`
In `(v)=(-R )/(m)((1)/(t))+c`
`2.303"log"[v(t)]=(-R )/(m)((1)/(t))+c`
The best way is to draw a plot between log [v(t)] against `((1)/(t))`