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......