The ratio of the distances travelled by a freely falling body in the 1 text st , 2 text nd , 3 text rd and 4 text th second :

Question

The ratio of the distances travelled by a freely falling body in the 1 text st , 2 text nd , 3 text rd and 4 text th second : (A) 1: 1: 1: 1 (B) 1: 2: 3: 4 (C) 1: 4: 9: 16 (D) 1: 3: 5: 7

Tardigrade Admin · Accepted Answer

S nth = u +( a /2)(2 n -1) =0+( a /2)(2 n -1) S nth propto(2 n -1) ⇒ S 1 st , S 2 nd , S 3 rd , S 4 th =[2(1)-1]:[2(2)-1]:[2(3)-1]:[2(4)-1] =1: 3: 5: 7

Q. The ratio of the distances travelled by a freely falling body in the $1^{st}, 2^{nd}, 3^{rd}$ and $4^{th}$ second :

$1 : 1 : 1 : 1$

$1 : 2 : 3 : 4$

$1 : 4 : 9 : 16$

$1 : 3 : 5 : 7$

$S_{n t h} = u + \frac{a}{2} (2 n - 1)$
$= 0 + \frac{a}{2} (2 n - 1)$
$S_{n t h} \propto (2 n - 1)$
$\Rightarrow S_{1 s t}, S_{2 n d}, S_{3 r d}, S_{4 t h}$
$= [2 (1) - 1] : [2 (2) - 1] : [2 (3) - 1] : [2 (4) - 1]$
$= 1 : 3 : 5 : 7$

Q. The ratio of the distances travelled by a freely falling body in the 1st ,2nd ,3rd and 4th second :

1:1:1:1

1:2:3:4

1:4:9:16

1:3:5:7