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An object 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

A
same, which is 28 seconds
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B
in the ratio of the square roots of the integers 1, 2, 3, …
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C
in the ratio of the difference in the square roots of the integers, i.e., 1,(21),(32),(43), ...
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D
in the ratio of the reciprocals of the square roots of the integers, i.e., 11,12,13, ...
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Solution

The correct option is C in the ratio of the difference in the square roots of the integers, i.e., 1,(21),(32),(43), ...
For 1st 1 m:
as u=0
s=12g(t1)2
1=5(t1)2
t1=15

For 2nd 1 m:
We need subtract the time taken by body to fall 1 m from the total time taken by the body to fall 2 m.
2=5T2, here T= total time
T=25
t2=Tt1=2515

Similarly,
for nth 1 m:
tn=n5n15

So the ratio will be:
t1:t2:t3: ... :tn=15:2515:3525: ...
t1:t2:t3: ... :tn=1:21:32: ...

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