Galileo's law of odd number: The distances traversed, during equal intervals of time, by a body falling from rest, stand to one another in the same ratio as the odd number beginning with unity [namelly, `1 : 3 :5 : 7`....]. Prove it.

Options

A. 1 : 3 : 5 : 7 : 9 : …
B. 2 : 4 : 6 : 8 : 10 : …
C. 1 : 4 : 7 : 10 : 13 : …
D. None of the above

Answer

A

Explanation

Here, u = 0, a = g
Distance travelled in nth second is given by
`D_(n)=u+(a)/(2)(2n-1)`
`therefore D_(n) prop(2n-1)`
`therefore D_(1):D_(2):D_(3):D_(4):D_(5)…=1:3:5:7:9:..`