A particle is dropped vertically from rest from a height. The time taken by it to fall through successive distances of 1 m each will then be 

(1) All equal, being equal to 2/g second

(2) In the ratio of the square roots of the integers 1, 2, 3.....

(3) In the ratio of the difference in the square roots of the integers i.e. 1,(21),(32),(43) ....

(4) In the ratio of the reciprocal of the square roots of the integers i.e.,. 11,12,13,14 

(3) h=ut+12gt21=0×t1+12gt12t1=2/g

Velocity after travelling 1m distance

v2=u2+2ghv2=(0)2+2g×1v=2g

For second 1 meter distance

1=2g×t2+12gt22gt22+22gt22=0

t2=22g±8g+8g2g=2±2g

Taking +ve sign t2=(22)/g

t1t2=2/g(22)/g=121 and so on.

Difficulty Level:

  • 8%
  • 8%
  • 76%
  • 10%