Question

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,(√2−√1),(√3−√2),(√4−√3), ...For 1st 1 m: as u=0 s=12g(t1)2 1=5(t1)2 t1=1√5 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=T−t1=√25−√15 Similarly, for nth 1 m: tn=√n5−√n−15 So the ratio will be: t1:t2:t3: ... :tn=√15:√25−√15:√35−√25: ... t1:t2:t3: ... :tn=√1:√2−√1:√3−√2: ...

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