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Q.

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

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a

all being equal to 2/9 second

b

in the ratio of the square roots of the integers 1,2,3,..

c

in the ratio of the difference in the square roots of the integers is 1,2-1,3-2,4-3...

d

in the ratio of the reciprocal of the square roots of the integers is 11,12,13,14

answer is C.

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Detailed Solution

As, h=ut+12gt2

1=0×t1+12gt12

t1=2/g

Velocity after travelling 1m distance

v2=u2+2gh

v2=02+2g×1

v=2g

For second 1 m distance 

1=2g×t2+12gt22

gt22+22gt2-2=0

t2=-22g±8g+8g2g

=-2±2g

Taking +ve sign, t2=2-2t/g

t1t2=2/g2-2/g=12-1 and so on.

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