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Question

# 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

A
All equal, being equal to 2g second
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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 reciprocal of the square roots of the integers i.e., 11,12,13,14
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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)...h=ut+12gt2⇒1=0×t1+12gt21⇒t1=√2g Velocity after travelling 1m distance v2=u2+2gh⇒v2=(0)2+2g×1⇒v=√2g For second 1 meter distance 1=√2g×t2+12gt22⇒gt22+2√2gt2−2=0 t2=−2√2g±√8g+8g2g=−√2±2√g Taking +ve sign t2=2−√2√g ∴ t1t2=√2g(2−√2)√g=1√2−1 and so on

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