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 displacement in three successive half second intervals are $S_{1}\ ,S_{2},{\ S}_{3}$. Then,
A) $S_{1}:S_{2}:S_{3}:1:5:9$
B) $S_{1}:S_{2}:S_{3}:1:2:3$
C) $S_{1}:S_{2}:S_{3}:1:1:1$
D) $S_{1}:S_{2}:S_{3}:1:3:5$
Explanation
(d) ($S^{'} \propto t^{2}.$ Now, $S_{1}^{'}:S_{2}^{'}:S_{3}^{'} :: \frac{1}{4}:1:\frac{9}{4}$ or 1:4:9
For successive intervals,
$S_{1}:S_{2}:S_{3} :: 1:(4 - 1):(9 - 4)$
${or\ \ S}_{1}:S_{2}:S_{3} :: 1:3:5$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.