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Question

# A particle 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
All equal, being equal to 2/g 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 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 first 1m1=12×g×t2t1=√2gFor first 1m2=12×g×t2t1=√2×√2gfor second 1mt2=t−t1=√2g(√2−√1)similarly,t3=√2g(√3−√2)Hence option c is correct.

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