INVERSE SQUARE LAW
● F ∝ 1/r².
~ Newton assume the motion of planet around the sun as circular then if a planet of mass 'm' revolves around the sun with constant speed 'v' at a mean distance 'r' then the contripetal force acting on it is given by : __
[F = mv²÷r]
>> F ∝ v²÷r ______________(i)
Again, the speed 'v' of a planet is given by ____
>> v = 2πr/T
[ r = distance of planet from sun.]
[ T = time taken to complete one revolution around the sun.]
>> v ∝ r/t [squaring both side we get ]
>> v² ∝ r²÷ t² [ multiply and divided by 'r' ]
>> v² ∝ r³/t²r
Here r³/t² is constant ,😁
>> v² ∝ 1/r ______________(ii)
Now putting (i) and (ii) we get__
>< F ∝ v²/r [v²=1/r]
>< F ∝ 1/r × 1/r
>< F ∝ 1/r² [proved 😄😄].
[📚] ~Padhte raho badhte raho~ [📚]
.....✒️✒️satyamraj......