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Physics · MOTION IN A STRAIGHT LINE

हिन्दी

Given 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:

  1. Both (A) and (R) are true and (R) is the correct explanation of (A).
  2. Both (A) and (R) are true but (R) is NOT the correct explanation of (A).
  3. (A) is true but (R) is false.
  4. (A) is false but (R) is true.

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.
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