if an object falling vertically from rest take t sec less and acquire a velocity of u ms^-1 more in falling through same distance on 2 planets having acceelerations due to gravity of 2g and 8g respectively,then prove u=4gt

                                  particle - 1                                           particle - 2

accln                           2g                                                           8g  

dis. travelled               h                                                             h

time taken                  T                                                            T - t

velocity gained           v                                                            v + u

now    for 1           h = gt²          .....................(i)

 for 2                 h=4g(T-t)²    ....................(ii)

for 1                    v² = 4gh  .............................(iii)

for 2                (v+u)² = 16gh ......................(4)

for 1                 v= 2gT  ............................(5)

 from i & ii T=2t

from iii & 4  v=u 

putting it in 5 we get u=4gt