Physics · MOTION IN A STRAIGHT LINE
हिन्दीGiven below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): The distances traversed by a body falling freely from rest during successive equal intervals of time are in the ratio \( 1 : 3 : 5 : 7 : \dots \). Reason (R): The distance covered by a uniformly accelerating body in the \( n^{\text{th}} \) second is directly proportional to \( (2n - 1) \). In the light of the above statements, choose the correct answer from the options given below:
Correct answer · Option 1
Both (A) and (R) are true and (R) is the correct explanation of (A).
Explanation
For motion from rest under constant acceleration \( g \), \( D_n = \frac{1}{2}g(2n-1) \). Thus \( D_n \propto (2n-1) \), giving ratios 1:3:5:7 for successive equal time intervals, which explains Galileo's law of odd numbers.