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Q.

A particle starting from rest falls from a certain height. Assuming that the value of acceleration due to gravity remains the same throughout motion, its displacements in three successive half second intervals are $S_{1}, S_{2}, S_{3} .$ Then,

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a

$S_{1} : S_{2} : S_{3} = 1 : 2 : 3$

b

$S_{1} : S_{2} : S_{3} = 1 : 3 : 5$

c

$S_{1} : S_{2} : S_{3} = 1 : 5 : 9$

d

$S_{1} : S_{2} : S_{3} = 1 : 1 : 1$

answer is D.

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Detailed Solution

As, $s' \propto t^{2}$

Now, $s_{1}^{'} : s_{2}^{'} : s_{3}^{'} = \frac{1}{4} : 1 : \frac{9}{4} o r 1 : 4 : 9$

For successive intervals,

$s_{1} : s_{2} : s_{3} = 1 : (4 - 1) : (9 - 4)$

or $s_{1} : s_{2} : s_{3} = 1 : 3 : 5$

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A particle starting from rest falls from a certain height. Assuming that the value of acceleration due to gravity remains the same throughout motion, its displacements in three successive half second intervals are S1, S2, S3. Then,