A particle is dropped from rest from a large height. Assume g to be constant throughout the motion. The time taken by it to fall through successive distances of 1 m each will be

Time taken to cover first r meter is given by n=12gtn2  or  tn=2ngTime taken to cover first (n + 1) m is given bytn+1=2(n+1)gSo time taken to cover (n + 1)th m is given by tn+1−tn=2(n+1)g−2ng=2g[n+1−n]This gives the required ratio as1,(2−1),(3−2),⋯, etc., (starting from n=0)