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,

Question

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, (A) S1: S2: S3=1: 5: 9 (B) S1: S2: S3=1: 2: 3 (C) S1: S2: S3=1: 1: 1 (D) S1: S2: S3=1: 3: 5

Tardigrade Admin · Accepted Answer

As , s' propto t2 Now, s1': s2': s3'=(1/4): 1: (9/4) or 1: 4: 9 For successive intervals, s1: s2: s3=1:(4-1):(9-4) or s1: s2: s3=1: 3: 5

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,

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

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

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

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

$A s, s^{'} \propto t^{2}$
Now, $s_{1}^{'} : s_{2}^{'} : s_{3}^{'} = \frac{1}{4} : 1 : \frac{9}{4}$ or $1 : 4 : 9$
For successive intervals,
$s_{1} : s_{2} : s_{3} = 1 : (4 - 1) : (9 - 4)$
or $s_{1} : s_{2} : s_{3} = 1 : 3 : 5$

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 S1​,S2​,S3​. Then,

S1​:S2​:S3​=1:5:9

S1​:S2​:S3​=1:2:3

S1​:S2​:S3​=1:1:1

S1​:S2​:S3​=1:3:5